相关论文: A characterization of $L_{2}$ mixing and hypercont…

The large deviations properties of trajectory observables for chaotic non-invertible deterministic maps as studied recently by N. R. Smith, Phys. Rev. E 106, L042202 (2022) and by R. Gutierrez, A. Canella-Ortiz, C. Perez-Espigares,…

Classical spectral graph theory characterizes graphs with logarithmic mixing time. In this work, we present a combinatorial characterization of graphs with constant mixing time. The combinatorial characterization is based on the small-set…

Let $\pi$ denote the intractable posterior density that results when the likelihood from a multivariate linear regression model with errors from a scale mixture of normals is combined with the standard non-informative prior. There is a…

We show that the distribution of the first return time $\tau$ to the origin, v, of a simple random walk on an infinite recurrent graph is heavy tailed and nonconcentrated. More precisely, if $d_v$ is the degree of v, then for any $t\geq1$…

The problem of estimating the coefficient of bivariate tail dependence is considered here from the robustness point of view; it combines two apparently contradictory theories of robust statistics and extreme value statistics. The usual…

We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of…

Hitting times provide a fundamental measure of distance in random processes, quantifying the expected number of steps for a random walk starting at node $u$ to reach node $v$. They have broad applications across domains such as network…

We consider dynamical percolation on the $d$-dimensional discrete torus of side length $n$, $\mathbb{Z}_n^d$, where each edge refreshes its status at rate $\mu=\mu_n\le 1/2$ to be open with probability $p$. We study random walk on the…

We investigate the properties of uniform doubly stochastic random matrices, that is non-negative matrices conditioned to have their rows and columns sum to 1. The rescaled marginal distributions are shown to converge to exponential…

We show that the existence of a "good"' coupling w.r.t. Hamming distance for any local Markov chain on a discrete product space implies rapid mixing of the Glauber dynamics in a blackbox fashion. More specifically, we only require the…

We consider the computational task of sampling a bit string $x$ from a distribution $\pi(x)=|\langle x|\psi\rangle|^2$, where $\psi$ is the unique ground state of a local Hamiltonian $H$. Our main result describes a direct link between the…

In this work, we develop a comparison procedure for the Modified log-Sobolev Inequality (MLSI) constants of two reversible Markov chains on a finite state space. Efficient comparison of the MLSI Dirichlet forms is a well known obstacle in…

Logarithmic Sobolev inequalities are a powerful way to estimate the rate of convergence of Markov chains and to derive concentration inequalities on distributions. We prove that the log-Sobolev constant of any isotropic logconcave density…

We consider a Markov chain $\{X_n\}_{n=0}^\8$ on $\R^d$ defined by the stochastic recursion $X_{n}=M_n X_{n-1}+Q_n$, where $(Q_n,M_n)$ are i.i.d. random variables taking values in the affine group $H=\R^d\rtimes {\rm GL}(\R^d)$. Assume that…

We study the so-called pinning model, which describes the behavior of a Markov chain interacting with a distinguished state. The interaction depends on an external source of randomness, called disorder, which can attract or repel the Markov…

Convergence to equilibrium of underdamped Langevin dynamics is studied under general assumptions on the potential $U$ allowing for singularities. By modifying the direct approach to convergence in $L^2$ pioneered by F. H\'erau and…

We extend our previous study of Markov chains on finite commutative rings (arXiv:1605.05089) to arbitrary finite rings with identity. At each step, we either add or multiply by a randomly chosen element of the ring, where the addition…

We show that the modified log-Sobolev constant for a natural Markov chain which converges to an $r$-homogeneous strongly log-concave distribution is at least $1/r$. Applications include a sharp mixing time bound for the bases-exchange walk…

This paper proposes a new approach to describe the stability of linear time-invariant systems via the torsion $\tau(t)$ of the state trajectory. For a system $\dot{r}(t)=Ar(t)$ where $A$ is invertible, we show that (1) if there exists a…

Consider the skew product $F:\mathbb{T}^2 \to \mathbb{T}^2$, $F(x,y)= (f(x),y+\tau(x))$, where $f:\mathbb{T}^1\to \mathbb{T}^1$ is a piecewise $\mathscr{C}^{1+\alpha}$ expanding map on a countable partition and $\tau:\mathbb{T}^1 \to…