Related papers: Central limit theorem for the solution of the Kac …
We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…
The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…
In 2010, Shiffman and Zelditch proved a central limit theorem (CLT) for smooth statistics of Gaussian random zeros in codimension one over compact K\"ahler manifolds. They raised the question of whether this result admits a two-fold…
Selberg's central limit theorem states that the values of $\log|\zeta(1/2+i \tau)|$, where $\tau$ is a uniform random variable on $[T,2T]$, is distributed like a Gaussian random variable of mean $0$ and standard deviation…
The problem of convergence in law of normed sums of exchangeable random variables is examined. First, the problem is studied w.r.t. arrays of exchangeable random variables, and the special role played by mixtures of products of stable laws…
Consider the initial-boundary value problem for the 2-speed Carleman model of the Boltzmann equation of the kinetic theory of gases set in some bounded interval with boundary conditions prescribing the density of particles entering the…
We establish central limit theorems for the position and velocity of the charged particle in the mechanical particle model introduced in the paper "Limit velocity for a driven particle in a random medium with mass aggregation"…
This paper is devoted to the study of mean-field limit for systems of indistinguables particles undergoing collision processes. As formulated by Kac \cite{Kac1956} this limit is based on the {\em chaos propagation}, and we (1) prove and…
We study the free central limit theorem for not necessarily identically distributed free random variables where the limiting distribution is the semicircle distribution. Starting from an estimate for the Kolmogorov distance between the…
We study the (weak) equilibrium problem arising from the problem of optimally stopping a one-dimensional diffusion subject to an expectation constraint on the time until stopping. The weak equilibrium problem is realized with a set of…
The applicability conditions of a recently reported Central Limit Theorem-based approximation method in statistical physics are investigated and rigorously determined. The failure of this method at low and intermediate temperature is proved…
The standard central limit theorem plays a fundamental role in Boltzmann-Gibbs statistical mechanics. This important physical theory has been generalized \cite{Tsallis1988} in 1988 by using the entropy $S_q = \frac{1-\sum_i p_i^q}{q-1}$…
We study the Cauchy Problem for the relativistic Boltzmann equation with near Vacuum initial data. Unique global in time "mild" solutions are obtained uniformly in the speed of light parameter $c \ge 1$. We furthermore prove that solutions…
Let $G$ be an $N \times N$ real matrix whose entries are independent identically distributed standard normal random variables $G_{ij} \sim \mathcal{N}(0,1)$. The eigenvalues of such matrices are known to form a two-component system…
We provide the first quantitative result of convergence to equilibrium in the context of the spatially homogeneous Boltzmann-Fermi-Dirac equation associated to hard potentials interactions under angular cut-off assumption, providing an…
We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…
We study multivariate generalizations of the $q$-central limit theorem, a generalization of the classical central limit theorem consistent with nonextensive statistical mechanics. Two types of generalizations are addressed, more precisely…
Suppose X is a random vector, that is distributed uniformly in some n-dimensional convex set. It was conjectured that when the dimension n is very large, there exists a non-zero vector u, such that the distribution of the real random…
Peng (2006) initiated a new kind of central limit theorem under sub-linear expectations. Song (2017) gave an estimate of the rate of convergence of Peng's central limit theorem. Based on these results, we establish a new kind of almost sure…
This paper investigates a local central limit theorem for a normalized sequence of random variables belonging to a fixed order Wiener chaos and converging to the standard normal distribution. We prove, without imposing any additional…