Related papers: Central limit theorems for a driven particle in a …

A central limit theorem is proved for some strictly stationary sequences of random variables that satisfy certain mixing conditions and are subjected to the "shrinking operators" $U_r(x):=[\max\{|x|-r,0\}]\cdot x/|x|,\ r \ge 0$. For…

Here we comment on the paper by Arthur D. Yaghjian, Phys. Rev. E 78, 046606 (2008) (arXiv:0805.0142). The author provides an equation of motion for a point charged particle in a certain regime of system parameters (on the other hand,…

We investigate the dependence of the center-of-mass tomogram of a system with many degrees of freedom $N$ on the Planck constant $\hbar $. It is shown that to use the central limit theorem under taking the limit $N\to +\infty $ one should…

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 present a general approach to establish the Central Limit Theorem with error bounds for sequential dynamical systems. The main tool we develop is the application to this setting of a projective metric on complex cones, following the…

We prove that the solution of the Kac analogue of Boltzmann's equation can be viewed as a probability distribution of a sum of a random number of random variables. This fact allows us to study convergence to equilibrium by means of a few…

We prove a central limit theorem with speed $n^{-1/2}$ for stationary processes satisfying a strong decorrelation hypothesis. The proof is a modification of the proof of a theorem of Rio. It is elementary but quite long and technical.

Through certain appropriate constructions, we establish periodic solutions in distribution for some stochastic differential equations with infinite-dimensional Levy noise. Additionally, we obtain the corresponding periodic measures and…

We prove a central limit theorem for the algebraic and dynamical degrees of a random composition of Cremona transformations.

This paper deals with Poisson processes on an arbitrary measurable space. Using a direct approach, we derive formulae for moments and cumulants of a vector of multiple Wiener-It\^o integrals with respect to the compensated Poisson process.…

The distribution of a Markov process with killing, conditioned to be still alive at a given time, can be approximated by a Fleming-Viot type particle system. In such a system, each particle is simulated independently according to the law of…

We prove moment inequalities for a class of functionals of i.i.d. random fields. We then derive rates in the central limit theorem for weighted sums of such randoms fields via an approximation by $m$-dependent random fields.

We consider a driven tagged particle in a symmetric exclusion process on Z with a removal rule. In this process, untagged particles are removed once they jump to the left of the tagged particle. We investigate the behavior of the…

We consider a system consisting of $n$ particles, moving forward in jumps on the real line. System state is the empirical distribution of particle locations. Each particle ``jumps forward'' at some time points, with the instantaneous rate…

This monograph introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting…

The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes. The central limit theorem and functional central limit theorem are obtained for martingale like random variables under…

The multivariate central limit theorems (CLT) for the volumes of excursion sets of stationary quasi-associated random fields on $\mathbb{R}^d$ are proved. Special attention is paid to Gaussian and shot noise fields. Formulae for the…

We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting…

We prove quenched versions of a central limit theorem, a large deviations principle as well as a local central limit theorem for expanding on average cocycles. This is achieved by building an appropriate modification of the spectral method…

In this paper, we establish an almost sure central limit theorem for a general random sequence under a strong approximation condition. Additionally, we derive the law of the iterated logarithm for the center of mass corresponding to a…