Related papers: Some Notes on Quantitative Generalized CLTs with S…
We introduce a new version of Stein's method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and concentration of measure. Unlike Skorokhod…
A novel class of methods for combining $p$-values to perform aggregate hypothesis tests has emerged that exploit the properties of heavy-tailed Stable distributions. These methods offer important practical advantages including robustness to…
We consider inhomogeneous square random matrices of size $N$ with independent entries of mean 0 and finite variance. We assume that the variance profile of this matrix is doubly stochastic and has a band-like structure with an appropriately…
The problem of efficiently generating random samples from high-dimensional and non-log-concave posterior measures arising from nonlinear regression problems is considered. Extending investigations from arXiv:2009.05298, local and global…
We improve the discretization technique for weighted Lorentz norms by eliminating all "non-degeneracy" restrictions on the involved weights. We use the new method to provide equivalent estimates on the optimal constant $C$ such that the…
We study the scaling properties of the non-equilibrium stationary states (NESS) of a reaction-diffusion model. Under a suitable smallness condition, we show that the density of particles satisfies a law of large numbers with respect to the…
The paper considers the wave equation, with constant or variable coefficients in $\R^n$, with odd $n\geq 3$. We study the asymptotics of the distribution $\mu_t$ of the random solution at time $t\in\R$ as $t\to\infty$. It is assumed that…
By using the spectrum of the underlying symmetric diffusion operator, the convergence in $L^p$-Wasserstein distance $\mathbb W_p (p\ge 1)$ is characterized for the empirical measure $\mu_t$ of non-symmetric subordinated diffusion processes…
We study invariance principles and convergence to a Gaussian limit for stochastic series of the form $S(c,Z)=\sum_{m=1}^{\infty }\sum_{\alpha _{1}<...<\alpha _{m}}c(\alpha _{1},...,\alpha _{m})\prod_{i=1}^{m}Z_{\alpha _{i}}$ where $Z_{k}$,…
In this paper we consider a branching particle system consisting of particles moving according to the Ornstein-Uhlenbeck process in $\Rd$ and undergoing a binary, supercritical branching with a constant rate $\lambda>0$. This system is…
In this article, the possibility of generating non-classical light due to Planck-scale effects is considered. For this purpose, a widely studied model of deformation of the Heisenberg uncertainty relation is applied to single-mode and…
Local time-stepping methods permit to overcome the severe stability constraint on explicit methods caused by local mesh refinement without sacrificing explicitness. In \cite{DiazGrote09}, a leapfrog based explicit local time-stepping…
The purpose of this paper is to analyze the distribution distance between random vectors derived from the magnitude of the analytic wavelet transform of the squared envelopes of Gaussian processes and their large-scale limits. When the…
We introduce a class of Boltzmann equations on the real line, which constitute extensions of the classical Kac caricature. The collisional gain operators are defined by smoothing transformations with quite general properties. By…
Level statistics are a useful probe for detecting symmetries and distinguishing integrable and non-integrable systems. I show by way of several examples that level statistics detect the presence of generalized symmetries that go beyond…
An upper bound for the Wasserstein distance is provided in the general framework of the Wiener-Poisson space. Is obtained from this bound a second order Poincar\'e-type inequality which is useful in terms of computations. For completeness…
Under reasonable algebraic assumptions and under an infinite second order moment assumption, we show that the logarithm of the norm (log-norm) of a product of random i.i.d. matrices with entries in $\mathbb{R}$ or in any other local field…
We prove the stability of entropy solutions of nonlinear conservation laws with respect to perturbations of the initial datum, the space-time dependent flux and the entropy inequalities. Such a general stability theorem is motivated by the…
We present a straightforward formulation of Stein's method for the semicircular distribution, specifically designed for the analysis of non-commutative random variables. Our approach employs a non-commutative version of Stein's heuristic,…
The aim of this paper is to prove the strong law of large numbers (SLLN) as well as the central limit theorem (CLT) for a class of vector-valued stochastic processes which arise as solutions of the stochastic evolution inclusion…