Related papers: CLT for Ornstein-Uhlenbeck branching particle syst…
Various quantum analogues of the central limit theorem, which is one of the cornerstones of probability theory, are known in the literature. One such analogue, due to Cushen and Hudson, is of particular relevance for quantum optics. It…
We study branching processes in an i.i.d. random environment, where the associated random walk is of the oscillating type. This class of processes generalizes the classical notion of criticality. The main properties of such branching…
The block counting process with initial state $n$ counts the number of blocks of an exchangeable coalescent ($\Xi$-coalescent) restricted to a sample of size $n$. This work provides scaling limits for the block counting process of regular…
We consider a class of interacting particle systems with values in $[0,\8)^{\zd}$, of which the binary contact path process is an example. For $d \ge 3$ and under a certain square integrability condition on the total number of the…
We study a class of one-dimensional particle systems with true (Bird type) binary interactions, which includes Kac's model of the Boltzmann equation and nonlinear equations for the evolution of wealth distribution arising in kinetic…
We re-derive the Nyquist theorem and Callen-Welton fluctuation-dissipation theorem (FDT) as a consequence of detailed balance principle applied to a harmonic oscillator. The usage of electrical notions in the beginning makes the…
For quantum lattice systems a Boltzmann-type evolution arrises according to results of Hugenholtz in the limit of N-scaled time evolution together with an interaction scaled as N^-1/2. According ti Illner-Neunzert this passage to an…
In this paper we study uniform versions of two limit theorems in random left truncation model (RLTM). The law of large numbers (LLN) and the central limit theorem (CLT) have been obtained under the bracketing entropy conditions in this…
We develop a rigorous theory of hard-sphere dynamics in the kinetic regime, away from thermal equilibrium. In the low density limit, the empirical density obeys a law of large numbers and the dynamics is governed by the Boltzmann equation.…
A properly scaled critical Galton-Watson process converges to a continuous state critical branching process $\xi(\cdot)$ as the number of initial individuals tends to infinity. We extend this classical result by allowing for overlapping…
In this paper, we establish a spatial central limit theorem for a large class of supercritical branching, not necessarily symmetric, Markov processes with spatially dependent branching mechanisms satisfying a second moment condition. This…
We investigate a Poisson-Nernst-Planck type system in three spatial dimensions where the strength of the electric drift depends on a possibly small parameter and the particles are assumed to diffuse quadratically. On grounds of the global…
It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate…
In these notes, we obtain new stability estimates for centered non-degenerate selfdecomposable probability measures on $\mathbb{R}^d$ with finite second moment and for non-degenerate symmetric $\alpha$-stable probability measures on…
We use martingale embeddings to prove a central limit theorem (CLT) for one-dimensional projections of high-dimensional random vectors in $\{-1,1\}^n$ satisfying a Poincar\'e inequality. We obtain a non-asymptotic error bound involving…
The empirical Orlicz norm based on a random sample is defined as a natural estimator of the Orlicz norm of a univariate probability distribution. A law of large numbers is derived under minimal assumptions. The latter extends readily to a…
We consider the statistical motion of a convex rigid body in a gas of N smaller (spherical) atoms close to thermodynamic equilibrium. Because the rigid body is much bigger and heavier, it undergoes a lot of collisions leading to small…
We study the condensation phenomenon for the invariant measures of the mean-field model of reversible coagulation-fragmentation processes conditioned to a supercritical density of particles. It is shown that when the parameters of the…
We prove central limit theorems (CLTs) for topological functionals of Bernoulli bond percolation on infinite graphs beyond the Euclidean lattice $\mathbb{Z}^{d}$. For quasi-transitive graphs of subexponential growth, we show that the number…
We show that the total number of collisions in the exchangeable coalescent process driven by the beta $(1,b)$ measure converges in distribution to a 1-stable law, as the initial number of particles goes to infinity. The stable limit law is…