Related papers: Central limit theorems for the $\mathbb{Z}^2$-peri…

In the general context of computable metric spaces and computable measures we prove a kind of constructive Borel-Cantelli lemma: given a sequence (constructive in some way) of sets $A_{i}$ with effectively summable measures, there are…

We prove a central limit theorem for a class of additive processes that arise naturally in the theory of finite horizon Markov decision problems. The main theorem generalizes a classic result of Dobrushin (1956) for temporally…

Lattice Boltzmann simulations have been very successful in simulating liquid-gas and other multi-phase fluid systems. However, the underlying second order analysis of the equation of motion has long been known to be insufficient to…

We consider a positive recurrent one-dimensional diffusion process with continuous coefficients and we establish stable central limit theorems for a certain type of additive functionals of this diffusion. In other words we find some…

We extend the recent spectral approach for quenched limit theorems developed for piecewise expanding dynamics under general random driving [DrFrGTVa18] to quenched random piecewise hyperbolic dynamics including some classes of billiards.…

We compute the Lyapunov exponent, generalized Lyapunov exponents and the diffusion constant for a Lorentz gas on a square lattice, thus having infinite horizon. Approximate zeta functions, written in terms of probabilities rather than…

We construct classes of two-dimensional aperiodic Lorentz systems that have infinite horizon and are 'chaotic', in the sense that they are (Poincar\'e) recurrent, uniformly hyperbolic, ergodic, and the first-return map to any scatterer is…

A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…

We give a general local central limit theorem for the sum of two independent random variables, one of which satisfies a central limit theorem while the other satisfies a local central limit theorem with the same order variance. We apply…

We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…

The evolution of a gas can be described by different models depending on the observation scale. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. In particular, for rarefied…

In this paper, we establish a central limit theorem for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfying a second moment condition. This central limit theorem generalizes and…

This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…

We show that the generalised Stieltjes constants may be represented by infinite series involving logarithmic terms. Some relations involving the derivatives of the Hurwitz zeta function are also investigated

In this work, a generalised version of the central limit theorem is proposed for nonlinear functionals of the empirical measure of i.i.d. random variables, provided that the functional satisfies some regularity assumptions for the…

We investigate superdiffusion for stochastic processes generated by nonuniformly hyperbolic system models, in terms of the convergence of rescaled distributions to the normal distribution following the abnormal central limit theorem, which…

This paper is devoted to the construction and study of an equilibrium Glauber-type dynamics of infinite continuous particle systems. This dynamics is a special case of a spatial birth and death process. On the space $\Gamma$ of all locally…

We investigate a scaling limit of gradient stochastic dynamics associated to Gibbs states in classical continuous systems on ${\mathbb R}^d, d \ge 1$. The aim is to derive macroscopic quantities from a given micro- or mesoscopic system. The…

Let $T: X\mapsto X$ be a deterministic dynamical system preserving a probability measure $\mu$. A dynamical Borel-Cantelli lemma asserts that for certain sequences of subsets $A_n\subset X$ and $\mu$-almost every point $x\in X$ the…

Lie-Poisson structure of the Lorenz'63 system gives a physical insight on its dynamical and statistical behavior considering the evolution of the associated Casimir functions. We study the invariant density and other recurrence features of…