Related papers: A central limit theorem for a new statistic on per…

Define the non-overlapping return time of a random process to be the number of blocks that we wait before a particular block reappears. We prove a Central Limit Theorem based on these return times. This result has applications to entropy…

In this paper we study the cycle descent statistic on permutations. Several involutions on permutations and derangements are constructed. Moreover, we construct a bijection between negative cycle descent permutations and Callan perfect…

We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…

We give a new, self-contained proof of the multidimensional central limit theorem using the technique of ``doubling variables," which is traditionally used to prove uniqueness of solutions of partial differential equations (PDEs). Our…

This is a note on some results of the central limit theorem for deterministic dynamical systems. First, we give the central limit theorem for martingales, which is a main tool. Then we give the main results on the central limit theorem in…

We introduce a new tool to study the spectral type of rank one transformations using the method of central limit theorem for trigonometric sums. We get some new applications.

Some of the more powerful results of mathematical statistics are becoming of increasing importance in statistical mechanics. Here the use of the central limit theorem in conjunction with the canonical ensemble is shown to lead to an…

Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then…

We consider a variant of the randomly reinforced urn where more balls can be simultaneously drawn out and balls of different colors can be simultaneously added. More precisely, at each time-step, the conditional distribution of the number…

We prove limit theorems for the number of fixed points occurring in a random pattern-avoiding permutation distributed according to a one-parameter family of biased distributions. The bias parameter exponentially tilts the distribution…

The Central Limit Theorem for Iterated Functions Systems on the circle is proved. We study also ergodicity of such systems.

We give optimal convergence rates in the central limit theorem for a large class of martingale difference sequences with bounded third moments. The rates depend on the behaviour of the conditional variances and for stationary sequences the…

Recently a new type of central limit theorem for belief functions was given in Epstein et al. [9]. In this paper, we generalize the central limit theorem in Epstein et al. [9] to accommodate general bounded random variables. These results…

This paper enhances the result of the work [G. Kozma, B. T\'oth, Ann. Probab. vol. 45 (2017) 4307-4347] . We prove the central limit theorem (in probability w.r.t. the environment) for the displacement of a random walker in divergence-free…

Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…

Given a positive integer $n$, consider a random permutation $\tau$ of the set $\{1,2,\ldots, n\}$. In $\tau$, we look for sequences of consecutive integers that appear in adjacent positions: a maximal such a sequence is called a block. Each…

An urn contains balls of d colors. At each time, a ball is drawn and then replaced together with a random number of balls of the same color. Assuming that some colors are dominated by others, we prove central limit theorems. Some…

We show how a central limit theorem for Poisson model random polygons implies a central limit theorem for uniform model random polygons. To prove this implication, it suffices to show that in the two models, the variables in question have…

We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that…

We prove a central limit theorem for linear triangular arrays under weak dependence conditions. Our result is then applied to the study of dependent random variables sampled by a $\bbZ$-valued transient random walk. This extends the results…