Papers

The Zak-OTFS carrier waveform is a pulse in the delay-Doppler (DD) domain, and given the input-output (I/O) relation at one DD point in a frame, we can predict the I/O relation at all other points. While it is simple to acquire the effective wireless channel with Zak-OTFS, the cost of embracing inter-carrier interference is equalization complexity. The cost of linear minimum mean-square error (LMMSE) equalization grows cubically with the frame size. We describe how to use channel knowledge to reduce equalization complexity. For any pulse shaping filter, and for fractional delays and Dopplers, we show that the DD channel matrix is unitarily similar, through the discrete Zak transform, to a time-domain (TD) matrix that is a weighted sum of cyclic delay and Doppler operators, where the weights are the taps of the effective channel. We also obtain a dual frequency-domain (FD) form through an additional Fourier transform. The TD matrix is banded with a width set by the delay spread that is independent of the Doppler spread, whereas the FD matrix is banded with a width set only by the Doppler spread. We design a receiver that reads off the two widths from the channel estimate, selects the cheaper domain, and solves the banded system exactly, using a bordered Cholesky factorization that treats the quasi-periodic wrap-around without sacrificing degrees of freedom. Filters that decay slowly need a few preconditioned conjugate gradient steps. We show that the complexity of equalization becomes linear in the frame size. Simulations match direct DD-LMMSE error rates with three to four orders of magnitude fewer multiplications. A single receiver handles channels with very different delay and Doppler characteristics.

This paper, we introduce and study biatomic systems in Hilbert spaces, a natural generalization of classical atomic systems; this new concept allows us to represent bounded linear operators using two Bessel sequences simultaneously. In addition, we establish equivalent characterizations of these systems, study their relationship with Bessel biframes and demonstrate the stability of the class under natural operations: duality with respect to the adjunct, orthogonal projections, unit operators and concatenation.

Expectiles are tail-sensitive distributional summaries with important applications in financial risk measurement and forecasting, yet statistical theory for their online estimation from dependent data remains limited. We study a one-pass, stochastic-gradient algorithm with constant learning rate $\gamma$ for estimating the marginal expectile of a stationary causal process. The recursion admits a unique stationary causal solution and geometrically forgets its initialization. Under short-range dependence, its last iterate is asymptotically Gaussian at the $\sqrt{\gamma}$ scale, with variance governed by the population curvature and the long-run variance of the expectile score. For long-memory linear processes the scale changes to $\gamma^{\beta-1/2}\ell(1/\gamma)$, with a Gaussian limit arising from a fractional Brownian motion integral. We further derive the joint long-memory limit for multiple expectile levels and characterize its limiting covariance structure. Various numerical experiments corroborate the predicted Gaussian approximations and regime-specific fluctuation scales.

We study the two-dimensional non-rotating primitive equations with positive horizontal and vertical viscosity and without thermal diffusion. Our main results are fourfold. First, for every integer \(s\ge4\), we prove that sufficiently small, compatible, doubly periodic \(H^s\) perturbations of a stably stratified rest state with an affine temperature profile generate unique global strong solutions; the horizontal velocity and temperature remain uniformly small at the initial Sobolev order despite the derivative loss in the full diagnostic vertical velocity, and strict stratification persists. Second, we establish an inverse-map conservation law that determines the terminal temperature solely from the initial temperature: the terminal label is identified as the normalized increasing rearrangement of the initial label modulo the vertical period, and the terminal perturbation admits a quadratic expansion with cubic remainder. Third, the limiting equilibrium uniquely minimizes the quadratic perturbation energy among compatible, strictly stratified states with the same periodic label distribution. Finally, we establish sharp algebraic decay in suitable lower-order Sobolev norms for both velocity components and for the temperature and pressure differences from equilibrium. Exact nonlinear solutions provide matching lower bounds, establishing optimality for uniform estimates over the small-data class. The proofs combine weighted energy methods, spectral analysis, and inverse-map identities.

We develop explicit second-order particle-in-cell (PIC) methods for the Vlasov–Ampère and Vlasov–Maxwell systems using the scalar auxiliary variable (SAV) approach. Two schemes are proposed for each system: a predictor-based scheme and a symmetric splitting scheme using a scaled electric field. The methods exactly preserve the discrete Gauss law and a modified total energy. Numerical experiments for electrostatic and electromagnetic problems demonstrate the expected dynamics as well as the conservation properties of both invariants.

A hereditary graph class has strongly edge-sublinear separators if, for some constant $0 \leqslant b < 1$, every graph in the class with $m$ edges admits a balanced separator of size $\mathcal O(m^b)$. We show that Max Weight Independent Set (MWIS) admits a deterministic quasipolynomial-time approximation scheme (QPTAS) on every such class. In particular, this applies to graphs excluding any fixed graph as an induced minor, by a separator theorem of Korhonen and Lokshtanov [SODA 2024]. Our theorem generalizes the QPTASes for axis-parallel rectangles [Adamaszek and Wiese, FOCS 2013] and polygons [Adamaszek, Har-Peled, and Wiese, JACM 2019], or equivalently for packing connected subgraphs of a planar graph [Pilipczuk, van Leeuwen, and Wiese, Algorithmica 2020]. It also generalizes the QPTAS for MWIS on hereditary classes with strongly sublinear separators measured in vertices [Dvořák, EJC 2018; Dvořák and Lahiri, ESA 2021], as well as the QPTASes for graphs excluding particular induced minors [Chudnovsky et al., arXiv 2025; Bonnet et al., SWAT 2026; Czyżewska et al., arXiv 2026].

Let $\NT(m,n)$ be the total number of parts in the partitions of $n$ with rank $m$, and let $\MW(m,n)$ be the total number of ones in the partitions of $n$ with crank $m$. Using the uniform generalized-rank estimate of Liu and Zhou, we establish asymptotic formulas for $NT(m,n)$ and $\MW(m,n)$. Put $\beta_n=\pi/\sqrt{6n}$ and $L_n=\log(1/\beta_n)$. For every fixed $A>0$, uniformly for $|m|\le A\sqrt n$, we prove \begin{align*} \NT(m,n)&=\frac{p(n)L_n}{4}\sech^2\!\left(\frac{\beta_nm}{2}\right) +O_A\!\bigl(p(n)\log L_n\bigr) \intertext{ and} \MW(m,n)&=\frac{p(n)}4\log(1+e^{-\beta_nm}) \sech^2\!\left(\frac{\beta_nm}{2}\right) +O_A\!\bigl(p(n)\sqrt{\beta_nL_n}\bigr). \end{align*}

Layer-wise post-training quantization methods let each layer compensate for the quantization error inherited from earlier layers. We ask under what assumptions such compensation guarantees a network output error no larger than without it. For linear networks of any depth, with the required calibration Gram matrices invertible, if the rounding error of each layer has zero conditional mean and a deterministic second-moment map common to both schemes, as under subtractive dither on an unbounded grid, then compensation with strengths in $[0,1]$ fixed in advance gives a mean-square output error no larger than no compensation, each scheme being followed along its own trajectory. The exact gain separates error removed directly from reduced excitation of later rounding noise. Outside this setting the comparison can fail. With rectified linear activations it fails for two independent reasons: noise changes activation states, and, even when no state changes, the correction moves error from samples on which a unit is inactive to samples on which it is active. With stable activations, commutators between the calibration projection and the activation patterns bound the excess. With a bounded codebook, even unique exact layer-wise minimizers with no overload can give a larger output error. For fixed rounding errors it already fails for two scalar linear layers, refuting a published universal guarantee. An exact residual identity gives the necessary and sufficient condition on a common layer input. All these comparisons hold the calibration input fixed. On two 8B models at 4 bits, fixed half-strength compensation beat uncompensated rounding in every model, text and draw tested, yet no rule for choosing the strength beat a layer-wise rule consistently, and lowering the full-network loss on the data used to choose did not reliably lower it on new text.

Households compare their living standard with others' and dislike changing it. We study consumption and investment when felicity depends on consumption relative to a benchmark, the population's geometric average consumption, and cuts in felicity weigh more than increases. Asset returns are exogenous. For finitely many types and arbitrary initial wealth and inherited standards, a mean field equilibrium exists under a weak interaction condition, and for fixed budget multipliers the benchmark is the fixed point of a contraction. In a complete market with common risk, a mean field equilibrium at empirical type frequencies is an exact Nash equilibrium of the finite game, for any preferences over relative consumption. We bound the gain from deviating when plans computed at another composition are used. We compute equilibria in which groups with different wealth, inherited standards, and loss aversion revise spending at different dates. With identical households and common risk, the unique symmetric equilibrium is the policy of a single loss averse household with modified curvature. In a baseline example, ignoring the inherited standard costs up to 17% of wealth, while small errors about the composition of the reference group cost less than 0.5%.

In this paper, we focus on the examples constructed by Kanenobu and provide new family knots with the same HOMFLYPT polynomial invariants, which are distinguished by the Kauffman polynomial.

We present two and three dimensional direct numerical simulations of planar intrusions injected from a continuously supplied, narrow source into a linearly stratified ambient at the level of neutral buoyancy. The evolution passes through three phases. A laminar leading vortex dipole first advances at constant speed with a varicose wave train behind it; the trailing jet then undergoes a sinuous instability whose initial growth rate and wavelength agree with inviscid unstratified planar-jet theory evaluated on the local jet; the flow finally relaxes into a buoyancy-controlled wedge whose area grows linearly in time. Three-dimensional simulations show that the transition remains organized by the planar instability, while three-dimensionality reshapes the near-source region into a slowly evolving, actively mixing zone that entrains an additional twenty to one hundred percent of the source flux depending on source width. Rescaled with this measured effective flux, the downstream intrusion collapses reasonably well onto the similarity solution for a wide-source intrusion.

Let $K$ be a number field of degree $n_K$, and let $h(K)$ denote the smallest absolute value of the imaginary part of a non-trivial zero of its Dedekind zeta function. In 1979, Hoffstein proved the unconditional bound $h(K)\leq 0.87+o(1)$ as $n_K\to\infty$. In a 1990 survey article, Odlyzko stated without proof that a different kernel in Weil's explicit formula could produce $h(K)\leq 0.54+o(1)$. No further improvement on Hoffstein's $0.87$ threshold accompanied by a published proof has since appeared. We choose a linear kernel and first show that Hoffstein's original parameters already yield the improved constant $0.825$. We then generalise his linear kernel method using Stechkin's trick and prove the unconditional bound $h(K)\leq 0.6+o(1)$ as $n_K\to\infty$, giving the best proved asymptotic bound to date.

A result by F.-T. Tu dating from 2011 states that the orders in a local matrix algebra of dimension four that can be written as a finite intersection of maximal orders are those having an Eichler Gorenstein closure. In a more recent paper, we gave a similar characterization for orders with a Bass Gorenstein closure. More precisely, we prove that these orders are the ones that can be written as a ghost intersection, i.e., the set of points defined over the base field of an intersection of maximal orders that is defined over a field extension. Although we proved this result only for the local four-dimensional matrix algebra, the statement makes sense also for a local quaternion division algebra, since the latter turns into a matrix algebra when we extend the base field to an even degree extension. In this work, we prove an analog of our previous result in the latter setting.

Splines on Weyl groups model the equivariant cohomology of regular semisimple Hessenberg varieties, and the natural group action on them encodes the monodromy action. The resulting representations are of great interest in algebraic combinatorics for their connections to Hecke algebra characters, LLT polynomials, and chromatic symmetric functions. We study the analogous construction for dihedral groups, which in general have no underlying geometry. Using purely algebraic methods, we show that these spline modules are free, construct explicit bases, and compute their Hilbert series, recovering the familiar properties of the geometric setting. We also determine the associated dihedral group representations completely. Unlike what is conjectured for the symmetric group case, these need not be permutation representations.

For discrete outcomes, a valid conditional quantile can have a hit probability different from its nominal level. Errors in different covariate groups can also cancel when residual signs are pooled. We study sequential audits that address both problems by testing the two inequalities that define quantile-set membership. The audit records whether each response falls below, equals, or exceeds its forecast. We derive the information projection for this three-outcome experiment and use continuous betting mixtures within the cells of a covariate tree. Context-tree weighting combines the resulting audits over all prunings, with an explicit finite-path oracle bound. Under iid alternatives with uniformly positive sign probabilities, a countable mixture of refining trees attains the full conditional sign-information rate. A matching upper bound shows that no valid evidence sequence based on the same observations can attain a larger almost-sure exponential rate. We also bound the information lost through covariate coarsening, derive a recurrence for the local mixtures, and discuss quantile selection and confidence-sequence inversion. Simulations show how partition resolution affects detection, and a held-out count-data example illustrates the difference between quantile validity and exact-hit calibration.

In this paper the generic behavior of the Jordan structure of symplectic matrices under low-rank structure-preserving transformations is considered. So far, only the case of rank-one perturbations was covered in the literature, and this result is now extended to the case of arbitrary rank $k$. As a key step toward the main result, it is shown that all symplectic matrices that differ from the identity by rank $k$ can be represented as a product of $k$ symplectic reflectors unless they are similar to a diagonalizable matrix having only the eigenvalues $\pm 1$.

Let $\mathcal{C}(\Phi)$ denote a subclass of class $ \mathcal{C}$ of convex functions in the unit disc $\mathbb{D}=\{z:|z|<1, z\in \mathbb{C}\}$ defined by \begin{equation*} {Re}\left \{1+ \frac{ zf^{\prime \prime}(z)}{f^{\prime}(z)}\right \} \prec \Phi(z), \end{equation*} where $\Phi$ represents the Ma–Minda function in $\mathbb{D}$. For $f\in\mathcal{C}(\Phi)$, we find the sharp estimates of $||\gamma_{2}|-|\gamma_{1}||$, where $\gamma_{1}$ and $\gamma_{2}$ are the first two logarithmic coefficients of $f$. The bound is also obtained for the inverse logarithmic coefficients $\Gamma_{1}$ and $\Gamma_{2}$. We then show that, under suitable conditions, the bounds for $||\gamma_{2}|-|\gamma_{1}||$ and $||\Gamma_{2}|-|\Gamma_{1}||$ are identical, which gives the invariance result between these functionals. We also present bounds for the differences for various classes of univalent functions by choosing particular function $\Phi$. Thus our results unify several results studied in the literature.

A proper coloring of Euclidean space is a coloring that assigns different colors to points at distance one. Using the planar character-law rigidity theorem of OpenAI, we prove that every finite proper coloring of $\R^3$ can be replaced by a proper Lebesgue-measurable coloring with the same number of colors. As a corollary we obtain that the ordinary and measurable chromatic numbers of $\R^3$ are equal, and both lie between $7$ and $15$.

Entanglement entropies of multipartite pure states satisfy linear inequalities; for stabilizer states, the backbone of quantum error correction, the achievable entropy vectors generate a convex cone. We show that, after a linear lift, the closure of this cone is exactly the self-dual slice of a classical object on one more element than there are parties: the closed cone generated by the rank functions of arrangements of subspaces over $\mathrm{GF}(d)$ for a prime local dimension $d$, and of subgroups of abelian groups of exponent dividing $d$ in general. This correspondence brings two features of rank inequalities into play. First, the purifier acts as an extra variable: already for five parties the stabilizer cone is strictly smaller than the quantum linear rank cone, with which earlier evidence suggested it might coincide; an explicit six-variable inequality witnesses the gap. Second, the characteristic of the field enters, so the cone depends on the local dimension. It does not for up to four parties. With enough parties, the cone of $\mathbb{Z}_d$ qudits is contained in that of $\mathbb{Z}_{d'}$ qudits if and only if $d$ divides $d'$, and already for six parties the logical zero state of Steane's code lies outside the stabilizer cone of every odd local dimension. For this last result we show that the seven-variable characteristic-dependent inequalities we checked all follow from Shannon inequalities on the self-dual slice, and instead transfer one of them through a family of subgroups derived from the Fano plane.

We demonstrate the well-known fact that the diagonal of a unit regular pentagon has length the golden ratio. While similar to other proofs, we provide a novel figure that we believe is particularly well-suited to achieve full understanding at a glance.

We construct a fixed triangular family of noncommutative polynomials that spans the joint cyclic module of a real symmetric pair from any prescribed vector. In dimension at most $N$, when the second matrix has spectral diameter at most $N-1$, the family has $N(N+1)/2$ members, degree at most $N-1$, and a shared arithmetic circuit of size $O(N^2)$. No rank-dependent choice of coefficients is made. The proof uses a rational differential connection with a small self-adjoint residue: a primitive polynomial exterior vector for an invariant subspace must have an integer degree smaller than one. For connected trees, the probes and the pointed adjacency–degree reconstruction theorem give one explicit self-adjoint polynomial $p_N\in\mathbb{Z}\langle a,d\rangle$ whose trace separates all trees of order at most $N$. Its circuit has $O(N^2)$ gates, formal degree at most $3N-2$, and polynomial bit complexity. Only the original adjacency and degree matrices, the identity, and ordinary matrix arithmetic are used. A separate integer sum-of-squares construction gives a fixed positive semidefinite representative on which the all-one vector is cyclic; its degree is $O(N^2)$. A linear trace-degree lower bound shows that the first construction has the correct asymptotic degree scale.

For an odd prime p, we study the change in matrix order under lifting from Z/p^k Z to Z/p^(k+1) Z. The first variation of the order defect is an affine translate of a cyclic adjoint transfer on sl_2(F_p). We classify the full-order transfer for every q in GL_2(F_p): its rank is 3 for scalar elements, 1 for nonscalar semisimple elements, 1 for nonscalar Jordan elements when p = 3, and 0 for nonscalar Jordan elements when p > 3. For a Jordan element q = lambda(I + U), U^2 = 0 and U != 0, the vanishing first-order transfer for p > 3 admits an exact higher-order refinement. Writing d = (p - 1)/2, the full-order perturbation has depth d when tr(UX) != 0, depth p - 1 when tr(UX) = 0 and X is not in the span of U, and vanishes identically for X in the span of U. For p = 3, among the 27 lifts of a nonscalar order-preserving parent with determinant fixed to +1 or -1, exactly 9 preserve its order and 18 triple it; after the first increase, every further lift triples the order. We also give a scalar obstruction criterion for order preservation among unrestricted Jordan lifts.

Let $1<s\le2$ and let $H_{s}[0,1]$ consist of the real-valued continuous functions on $[0,1]$ whose graphs have Hausdorff dimension $s$. We prove that every finite-dimensional subspace $E\subset C[0,1]$ with $E\setminus\{0\}\subset H_{s}[0,1]$ is contained in a closed complemented subspace isomorphic to $c_0$, all of whose nonzero elements still belong to $H_{s}[0,1]$. This settles a question of Liu, Shi and Zhang. We also obtain the exact criterion: $H_{s}[0,1]$ is $(\alpha,\mathfrak{c})$-spaceable precisely when $\alpha$ is finite. We also show that every admissible finite-dimensional subspace is contained in a dense subspace of Hamel dimension $\mathfrak{c}$ whose nonzero elements have the same prescribed graph dimension. This also recovers maximal pointwise dense-lineability of $H_{s}[0,1]$.

We deduce zero-density estimates in short vertical strips from short-interval moments of globally tempered automorphic $L$-functions, by adapting the large-value estimate of Guth and Maynard and the Type II zero argument of Maynard and Pratt to the framework of Ye and Zhang. For the Riemann zeta function, we obtain $N_\zeta(\sigma;T,T+T^a)\ll T^{15a(1-\sigma)/(3+5\sigma)+\varepsilon}$ for $2/3\le a\le1$ and $7/10\le\sigma\le4/5$, improving Ye–Zhang's exponent in the interior of this range. Combining the localized density bound with the recent quasi-Riemann theorems, we estimate smoothed prime-power sums with phase $\exp(2\pi i\alpha n^\beta)$ on intervals of length $K^\delta$. For $0<\beta<13/20$, we obtain a power saving whenever $\max\{17/30,1-\beta\}<\delta<1$; in particular the square-root phase admits every $\delta>17/30$. A revised transform estimate retains both the stationary spread and the Fourier width $K/L$. For example, the bound at $\beta=1/2$, $\delta=3/5$ is $K^{15/26+\varepsilon}$, uniformly for frequencies $m\alpha$ with $1\le m\le K^{1/10}$. We also retain power savings for certain self-dual $GL(2)$ twists and self-dual $GL(3)$ cusp forms, without assuming Ramanujan. All three applications have explicit frequency dependence.

We generalize Moser's stability theorem for minimal hypersurface foliations to arbitrary codimension. Let $\mathbb{T}^N=\mathbb{R}^N/\mathbb{Z}^N$ be the standard torus, and let $P\subset\mathbb{R}^N$ be an $m$-plane satisfying a Diophantine condition relative to $\mathbb{Z}^N$. We prove that, under every sufficiently small smooth $\mathbb{Z}^N$-periodic perturbation of the Euclidean metric, the affine foliation of $\mathbb{T}^N$ induced by $P$ persists as a smoothly conjugate foliation by minimal $m$-dimensional submanifolds. The normalized conjugating displacement depends smoothly and tamely on the metric and is locally unique. The proof uses Hamilton's formulation of the Nash-Moser implicit function theorem.

In nonparametric density estimation without privacy constraints, it is known that a confidence set whose coverage holds uniformly over a `rough' class of regularity $r\geq0$ can simultaneously attain, in $L^2$-diameter, the minimax rate over a smaller, smoother class of regularity $s>r$ if and only if $s \le 2r$. We study such adaptive honest confidence sets under non-interactive $\alpha$-local differential privacy (LDP) constraints. Our main result is that, for bounded $\alpha$, such `smooth-rate adaptation' is now possible if and only if $s \le 4r/3$. In this smaller range we construct an honest private confidence set whose diameter is of the private minimax order on each of the two classes. As in the non-private case, the threshold arises because an honest set cannot, at a smooth density, be narrower than the separation rate arising in a related testing problem. Under LDP we prove that this private testing rate is of order $(n\alpha^2)^{-2r/(4r+3)}$, which is at most the private estimation rate $(n\alpha^2)^{-s/(2s+2)}$ over the smooth class exactly when $s \le 4r/3$. For $s > 4r/3$, however, we show that smooth-rate adaptation becomes possible once one discards from the rough class the densities that lie outside the smooth class but within an $L^2$-radius of the order of the private testing rate.

We prove that round circles $C_L$ are the unique minimisers of integral Menger curvature among embedded closed $C^1$ curves $\gamma$ of prescribed length $L$ for every $p\geq 2$, i.e. $M_p(C_L) \leq M_p(\gamma)$, with equality if and only if $\gamma$ parametrises a round circle. The proof combines a three-point symmetrisation, an analysis of diagonal truncations, and the periodic Wirtinger inequality. For $p>3$, known self-avoidance and regularity results extend the minimisation result to closed rectifiable curves without assuming embeddedness or smoothness, provided the length of the curve image equals $L$. In particular, $M_p$ detects the unknot and is basic for $p>3$, thereby answering a question posed repeatedly in the literature.

Let $g$ be a fixed primitive Hecke–Maass cusp form, and let $f$ vary with spectral parameter $k_f=K$, at a fixed level and with trivial nebentypus. We study smooth sums of $\lambda_f(n)\lambda_g(n)e(\alpha n^\beta)$ for fixed real $\alpha\ne0$. The crucial input is the smooth spectral second moment of Lau, Liu, and Ye, for which the window length can be taken to be $L=K^{1/3+a}$ for arbitrarily small fixed $a>0$. We show that, for every $\kappa>0$, there is $\beta_0>0$ such that the sum is $O(K^{2/3+\kappa}X^{1/2})$ for $1\le X\le K^2$ and $0<\beta\le\beta_0$. We give a detailed Baire category argument which makes the dependence on the smooth weight uniform through one finite derivative norm. A second argument keeps the phase explicit, applies Voronoi summation and shifted convolution estimates, and gives the numerical bound $O(K^{423/224+(5/7)\beta+\varepsilon})$ at $X=K^2$ for $0<\beta<5/32$.

This paper investigates a new role of randomness in stochastic policies–as a medium for embedding and communicating information. Specifically, we consider an agent interacting with an environment according to a prescribed stochastic policy. By carefully modulating the random action realizations of the policy, information can be embedded into the agent's behavior without altering the prescribed action distribution. We cast this problem as a channel coding problem, in which the controlled system implicitly serves as a communication channel. We then propose a coding scheme, termed posterior-matching randomness modulation (PRAM), that selects actions according to the message to be transmitted. With the aid of common randomness independent of the control system, PRAM preserves the prescribed action distribution for every state and every message. We further prove that PRAM is asymptotically reliable: the message can be decoded with arbitrarily small error probability as the observed state trajectory becomes sufficiently long. Experiments demonstrate the effectiveness of the proposed framework in applications including multi-bit policy watermarking and trajectory provenance.

The median-of-means (MoM) estimator is a robust alternative to the sample mean for heavy-tailed or contaminated data. While its non-asymptotic properties are well understood for i.i.d.\ samples, much less is known for dependent sequences. We establish non-asymptotic deviation bounds for the MoM estimator computed from consecutive blocks of an identically distributed $\alpha$-mixing sequence, both for a single mean and uniformly over a class of functions (the median-of-means process). All bounds remain valid, with explicitly adjusted constants, when a sufficiently small fraction of the blocks is adversarially corrupted. As applications, we obtain deviation bounds for a median-of-means Nadaraya–Watson regression estimator, for the MoM kernel density estimator, and for empirical and Bahadur-type estimators of Value-at-Risk and Conditional Value-at-Risk. Finally, we show that the sampling of bulk materials, where the measurements form a spatially dependent random field, reduces to the one-dimensional setting if the samples are taken in well-separated groups.