arXiv subjects

Hanchao Wang

Publications and source records attributed to Hanchao Wang.

At least 19 recordsLinked to original sources

arXiv2026

Majorizing Measures for Canonical Processes with Log-Concave Tails

Let $Y_1,\ldots,Y_n$ be independent symmetric random variables with log-concave tails. We give a dimension-free characterization of the expected supremum of the canonical process $X_x=\sum_{i=1}^n x_iY_i$ without any $Δ_2$ or regular-growth assumption on the coordinate tails. The characterization is governed by scale-dependent intrinsic costs determined directly by the convex tail potentials. It has an information-theoretic rate-distortion formulation as well as two equivalent majorizing-measure formulations on the original index set, one multiscale and one based on a single probability measure. More strongly, the comparison holds for every prescribed law of the index. In particular, the Gaussian majorizing-measure theorem of Talagrand and the Bernoulli theorem of Bednorz-Latała are recovered from the same formula, through quadratic and truncated quadratic costs, respectively. The new geometry is necessary: once the $Δ_2$ growth condition is removed, the usual chaining functional based on increment moments can exceed the expected supremum by an unbounded factor. The proof is based on a uniform convex-order truncation principle for symmetric exponentials and a dyadic decomposition of the tail slopes that transfers simultaneously the random process and its intrinsic cost, with universal constants.

math.PR↗

arXiv2026

Rank deficiency of Bernoulli random matrices for growing corank

Let A be an n x n Bernoulli random matrix whose entries are i.i.d. Bernoulli(p) random variables. In this paper, we determine the probability that the corank of A is at least k when k is of order o(sqrt(log n)): P(corank A >= k) = (1-p+o_n(1))^(kn).

math.PR↗

arXiv2026

Failure of Convex-Hull Bounds under Log-Convex Tails

Fix $0 t)=e^{-t^r},\qquad t\ge 0. \] We prove that there is no constant $C_r$, depending only on $r$, with the following universal property: for every finite set $T\subset \R^N$ there exists a sequence $(y_k)_{k\ge 1}\subset \R^N$ such that \[ T-T\subset conv\{y_k:k\ge 1\}, \qquad \|X_{y_k}\|_{L_{\log(k+2)}}\le C_r\,\bx(T) \quad (k\ge 1), \] where $X_t=\sum_i t_i X_i$ and $\bx(T)=\textsf{E}\sup_{t\in T}X_t$. This gives a negative answer to a question of Latała concerning the validity of convex-hull bounds for canonical Weibull processes. In fact, the failure persists even when the auxiliary vectors appearing in the convex hull are allowed to be arbitrary.

math.FA↗

arXiv2026

The Dual Majorizing Measure Theorem for Canonical Processes

We give a dual, separated-tree formulation of Latala's majorizing measure theorem for canonical processes with log-concave tails. Under the same assumptions as in Latala's characterization, we introduce parameterized separation trees and prove that the expected supremum is equivalent, up to universal constants, to the corresponding tree functional. We also develop a pointwise growth condition, inspired by the contraction principle, which leads to a deterministic polynomial-time algorithm for approximating the expected supremum when the index set is finite.

math.PR↗

arXiv2026

Error bounds of Median-of-means estimators with VC-dimension

We obtain the upper error bounds of robust estimators for mean vector, using the median-of-means (MOM) method. The method is designed to handle data with heavy tails and contamination, with only a finite second moment, which is weaker than many others, relying on the VC dimension rather than the Rademacher complexity to measure statistical complexity. This allows us to implement MOM in covariance estimation, without imposing conditions such as $L$-sub-Gaussian or $L_{4}-L_{2}$ norm equivalence. In particular, we derive a new robust estimator, the MOM version of the halfspace depth, along with error bounds for mean estimation in any norm.

math.ST↗

arXiv2026

The eigenvalue gap of inhomogeneous symmetric discrete random matrix

Let A be an n x n symmetric random matrix whose upper-triangular entries are independent and follow possibly non-identical subgaussian distributions. This paper investigates the spectral properties of A, including its eigenvalues and eigenvectors. Firstly, we prove that for k <= n / log n, 1 <= i <= n - k and epsilon >= 0, P(the gap between the (i+k)-th and i-th eigenvalues is at most epsilon n^(-1/2)) <= (C epsilon)^((k^2 + k)/2) + exp(-c n), where the eigenvalues are ordered increasingly. Secondly, combining the recent result of Yi Han, we give a quantitative estimate of the singular values of A. For c log n <= k <= sqrt(n) and epsilon >= 0, we have P(the (n-k+1)-th smallest singular value of A is at most k epsilon n^(-1/2)) <= (C epsilon)^(c k^2) + exp(-c k n), where the singular values are ordered increasingly. Finally, based on the distance analytical framework developed for the eigenvalue gap, we further derive quantitative bounds for singular values and delocalization of eigenvectors. In particular, we establish a quantitative bound for the probability that some eigenvector of A exhibits no-gap delocalization, which improves the result of Rudelson and Vershynin.

math.PR↗

arXiv2026

Tango: Taming Visual Signals for Efficient Video Large Language Models

Token pruning has emerged as a mainstream approach for developing efficient Video Large Language Models (Video LLMs). This work revisits and advances the two predominant token-pruning paradigms: attention-based selection and similarity-based clustering. Our study reveals two critical limitations in existing methods: (1) conventional top-k selection strategies fail to fully account for the attention distribution, which is often spatially multi-modal and long-tailed in magnitude; and (2) direct similarity-based clustering frequently generates fragmented clusters, resulting in distorted representations after pooling. To address these bottlenecks, we propose Tango, a novel framework designed to optimize the utilization of visual signals. Tango integrates a diversity-driven strategy to enhance attention-based token selection, and introduces Spatio-temporal Rotary Position Embedding (ST-RoPE) to preserve geometric structure via locality priors. Comprehensive experiments across various Video LLMs and video understanding benchmarks demonstrate the effectiveness and generalizability of our approach. Notably, when retaining only 10% of the video tokens, Tango preserves 98.9% of the original performance on LLaVA-OV while delivering a 1.88$\times$ inference speedup.

cs.CV↗

arXiv2026

The exact group-sparse recovery for block diagonal matrices with subexponential entries

We study block-diagonal random matrices with i.i.d. subexponential entries and show that, despite their highly structured form, they already guarantee exact sparse recovery from a nearly optimal number of measurements. When the matrix reduces to a single block, our framework collapses to the classical i.i.d. subexponential ensemble, and our bounds recover the well-known optimal rates previously established for unstructured random matrices.

math.PR↗

arXiv2026

Uniform Concentration for $α$-subexponential Random Operators

Random matrices acting on structured sets play a fundamental role in high-dimensional geometry, compressed sensing, and randomized algorithms. Existing results primarily focus on subgaussian models, when random matrices act as near-isometries on sets with optimal tail behavior. Nevertheless, very often in applications we deal with distributions with heavy tails that are not subgaussian but have at least exponential-type tails. In this work, we study random matrices A whose rows (or columns) have $α$-subexponential tail distributions with $α\in (0,2]$. So subgaussian and sub-exponential models are included in as special cases. We establish concentration type inequality for $Ax$, where x belongs to the bounded subsets of $\mathbb{R}^n$, showing that their geometric distortion is governed by Talagrand's functional of the set and depends on the tail parameter $α$. Our results extend the known optimal inequalities in the subgaussian regime ($α=2$), and provide new guarantees for heavier-tailed, yet exponentially integrable, random matrices. These findings extend the theory of random matrices beyond the subgaussian framework. Moreover, they yield near-isometric embedding results applicable to dimension reduction and allow us to make robust high-dimensional inference under non-Gaussian measurements.

math.PR↗

arXiv2025

Central Limit Theorem for Irregular Discretization Scheme of Multilevel Monte Carlo Method

In this paper, we study the asymptotic error distribution for a two-level irregular discretization scheme of the solution to the stochastic differential equations (SDE for short) driven by a continuous semimartingale and obtain a central limit theorem for the error processes with the rate $\sqrt{n}$. As an application, in the spirit of the result of Ben Alaya and Kebaier, we get a central limit theorem of the Linderberg-Feller type for the irregular discretization scheme of the multilevel Monte Carlo method.

math.PR↗

arXiv2025

MERba: Multi-Receptive Field MambaVision for Micro-Expression Recognition

Micro-expressions (MEs) are brief, involuntary facial movements that reveal genuine emotions, offering valuable insights for psychological assessment and criminal investigations. Despite significant progress in automatic ME recognition (MER), existing methods still struggle to simultaneously capture localized muscle activations and global facial dependencies, both essential for decoding subtle emotional cues. To address this challenge, we propose MERba, a hierarchical multi-receptive field architecture specially designed for MER, which incorporates a series of Local-Global Feature Integration stages. Within each stage, detailed intra-window motion patterns are captured using MERba Local Extractors, which integrate MambaVision Mixers with a tailored asymmetric multi-scanning strategy to enhance local spatial sensitivity. These localized features are then aggregated through lightweight self-attention layers that explicitly model inter-window relationships, enabling effective global context construction. Furthermore, to mitigate the challenge of high inter-class similarity among negative MEs, we introduce a Dual-Granularity Classification Module that decomposes the recognition task into a coarse-to-fine paradigm. Extensive experiments on three benchmark datasets demonstrate that MERba consistently outperforms existing methods, with ablation studies confirming the effectiveness of each proposed component.

cs.HC↗

arXiv2025

Quantitative estimates of the spectral norm of random matrices with independent columns

This paper investigates the nonasymptotic properties of the spectral norm of some random matrices with independent columns. In particular, we consider an $m\times n$ random matrix $BA$, where $A$ is an $N\times n$ random matrix with independent mean-zero subexponential entries, and $B$ is an $m\times N$ deterministic matrix. We prove that the $L_{p}$ norm of the spectral norm of $BA$ is upper bounded by $(\sqrt{m}+\sqrt{n})p$. It is remarkable that this result is independent of the dimension $N$.

math.PR↗

arXiv2025

The Rank and Singular Values of the Inhomogeneous Subgaussian Random Matrices

Let A be an n*n random matrix with mean zero and independent inhomogeneous non-constant subgaussian entries. We get that for any k<c\sqrt{n}, the probability of the matrix has a lower rank than n-k that is sub-exponential. Furthermore, we get a deviation inequality for the singular values of A. This extends earlier results of Rudelson's paper in 2024 by removing the assumption of the identical distribution of the entries across the matrix. Our model covers inhomogeneous matrices, allowing different subgaussian moments for the entries as long as their subgaussian moments have a standard upper bound. In the past advance, the assumption of i.i.d entries was required due to the lack of least common denominators of the non-i.i.d random matrix. We can overcome this problem using a randomized least common denominator (RLCD) from Livshyts in 2021.

math.PR↗

arXiv2024

Quantitative estimates of the singular values of random i.i.d. matrices

Let $M$ be an $n\times n$ random i.i.d. matrix. This paper studies the deviation inequality of $s_{n-k+1}(M)$, the $k$-th smallest singular value of $M$. In particular, when the entries of $M$ are subgaussian, we show that for any $γ\in (0, 1/2), \varepsilon>0$ and $\log n\le k\le c\sqrt{n}$ \begin{align} \textsf{P}\{s_{n-k+1}(M)\le \frac{\varepsilon}{\sqrt{n}} \}\le \Big( \frac{C\varepsilon}{k}\Big)^{γk^{2}}+e^{-c_{1}kn}.\nonumber \end{align} This result improves an existing result of Nguyen, which obtained a deviation inequality of $s_{n-k+1}(M)$ with $(C\varepsilon/k)^{γk^{2}}+e^{-cn}$ decay.

math.PR↗

arXiv2024

On Log-Concave-Tailed Chaoses and the Restricted Isometry Property

In this paper, we obtain a $p$-th moment bound for the suprema of a log-concave-tailed nonhomogeneous chaos process, which is optimal in some special cases. A crucial ingredient of the proof is a novel decoupling inequality, which may be of independent interest. With this $p$-th moment bound, we show two uniform Hanson-Wright type deviation inequalities for $α$-subexponential entries ($1\le α\le 2$), which recover some known results. As applications, we prove the restricted isometry property of partial random circulant matrices and time-frequency structured random matrices induced by standard $α$-subexponential vectors ($1\le α\le 2$), which extends the previously known results for the subgaussian case.

math.PR↗

arXiv2023

On Talagrand's functional and generic chaining

In the study of the supremum of stochastic processes, Talagrand's chaining functionals and his generic chaining method are heavily related to the distribution of stochastic processes. In the present paper, we construct Talagrand's type functionals in the general distribution case and obtain the upper bound for the suprema of all $p$-th moments of the stochastic process using the generic chaining method. As applications, we obtained the Johnson-Lindenstrauss lemma, the upper bound for the supremum of all $p$-th moment of order 2 Gaussian chaos, and convex signal recovery in our setting.

math.PR↗

arXiv2023

Tail Bounds on the Spectral Norm of Sub-Exponential Random Matrices

Let $X$ be an $n\times n$ symmetric random matrix with independent but non-identically distributed entries. The deviation inequalities of the spectral norm of $X$ with Gaussian entries have been obtained by using the standard concentration of Gaussian measure results. This paper establishes an upper tail bound of the spectral norm of $X$ with sub-Exponential entries. Our method relies upon a crucial ingredient of a novel chaining argument that essentially involves both the particular structure of the sets used for the chaining and the distribution of coordinates of a point on the unit sphere.

math.PR↗

arXiv2023

Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data

In this paper, we consider estimating spot/instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalised shrinkage technique in the matrix estimation for noise-free data under a uniform sparsity assumption, a natural extension of the approximate sparsity commonly used in the literature. The uniform consistency property is derived for the proposed spot volatility matrix estimator with convergence rates comparable to the optimal minimax one. For the high-frequency data contaminated by microstructure noise, we introduce a localised pre-averaging estimation method that reduces the effective magnitude of the noise. We then use the estimation tool developed in the noise-free scenario, and derive the uniform convergence rates for the developed spot volatility matrix estimator. We further combine the kernel smoothing with the shrinkage technique to estimate the time-varying volatility matrix of the high-dimensional noise vector. In addition, we consider large spot volatility matrix estimation in time-varying factor models with observable risk factors and derive the uniform convergence property. We provide numerical studies including simulation and empirical application to examine the performance of the proposed estimation methods in finite samples.

econ.EM↗