Related papers: Propagation of Localization Optimal Entropy Produc…
It is well known that central order statistics exhibit a central limit behavior and converge to a Gaussian distribution as the sample size grows. This paper strengthens this known result by establishing an entropic version of the CLT that…
A quantum analogue of the Central Limit Theorem (CLT) for bosonic system, first introduced by Cushen and Hudson (1971), states that the $n$-fold convolution $\rho^{\boxplus n}$ of an $m$-mode quantum state $\rho$, with zero first moments…
We study the convergence in distribution norms in the Central Limit Theorem for non identical distributed random variables that is $$ \varepsilon_{n}(f):={\mathbb{E}}\Big(f\Big(\frac 1{\sqrt…
A local convergence rate is established for a Gauss orthogonal collocation method applied to optimal control problems with control constraints. If the Hamiltonian possesses a strong convexity property, then the theory yields convergence for…
We introduce a new method for obtaining quantitative convergence rates for the central limit theorem (CLT) in a high dimensional setting. Using our method, we obtain several new bounds for convergence in transportation distance and entropy,…
We prove several fundamental statistical bounds for entropic OT with the squared Euclidean cost between subgaussian probability measures in arbitrary dimension. First, through a new sample complexity result we establish the rate of…
We prove a local central limit theorem (LCLT) for the number of points $N(J)$ in a region $J$ in $\mathbb R^d$ specified by a determinantal point process with an Hermitian kernel. The only assumption is that the variance of $N(J)$ tends to…
We consider the problem of optimal transportation with general cost between a empirical measure and a general target probability on R d , with d $\ge$ 1. We extend results in [19] and prove asymptotic stability of both optimal transport…
For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian…
This paper shows how to evolve numerically the maximum entropy probability distributions for a given set of constraints, which is a variational calculus problem. An evolutionary algorithm can obtain approximations to some well-known…
We show that the centered maximum of a sequence of log-correlated Gaussian fields in any dimension converges in distribution, under the assumption that the covariances of the fields converge in a suitable sense. We identify the limit as a…
Maxwell's velocity distribution is known to be universally valid across systems and phases. Here we present a new and general derivation that uses the central limit theorem (CLT) of the probability theory. This essentially uses the idea…
We describe a maximum entropy approach for computing volumes and counting integer points in polyhedra. To estimate the number of points from a particular set X in R^n in a polyhedron P in R^n, by solving a certain entropy maximization…
We consider the rates of convergence of the quenched central limit theorem for hitting times of one-dimensional random walks in a random environment. Previous results had identified polynomial upper bounds for the rates of decay which are…
We provide the first quantitative estimates for the rate of convergence in the free multiplicative central limit theorem (CLT), in terms of the Kolmogorov and $r$-Wasserstein distances for $r \geq 1$. While the free additive CLT has been…
We show how the renormalization group approach can be used to prove quantitative central limit theorems (CLTs) in the setting of free, Boolean, bi-free and bi-Boolean independence under finite third moment assumptions. The proofs rely on…
We prove a central limit theorem for the entropic transportation cost between subgaussian probability measures, centered at the population cost. This is the first result which allows for asymptotically valid inference for entropic optimal…
A local convergence rate is established for an orthogonal collocation method based on Gauss quadrature applied to an unconstrained optimal control problem. If the continuous problem has a sufficiently smooth solution and the Hamiltonian…
The Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of $n$ mutually independent and identically distributed random variables with finite first and…
The question of whether the central limit theorem (CLT) holds for the total number of edges in exponential random graph models (ERGMs) in the subcritical region of parameters has remained an open problem. In this paper, we establish the…