Related papers: Noncentral limit theorem for the generalized Rosen…

We focus on the FeigenbaumCoulletTresser point of the dissipative one-dimensional z logistic map. We show that sums of iterates converge to q Gaussian distributions, which optimize the nonadditive entropic functional Sq under simple…

By using chaos expansion into multiple stochastic integrals, we make a wavelet analysis of two self-similar stochastic processes: the fractional Brownian motion and the Rosenblatt process. We study the asymptotic behavior of the statistic…

We introduce a framework to derive quantitative central limit theorems in the context of non-linear approximation of Gaussian random variables taking values in a separable Hilbert space. In particular, our method provides an alternative to…

The (BC type) z-measures are a family of four parameter $z, z', a, b$ probability measures on the path space of the nonnegative Gelfand-Tsetlin graph with Jacobi-edge multiplicities. We can interpret the $z$-measures as random point…

We establish uniform pointwise estimates for the densities of a family of $\alpha$-stable processes with respect to the index $\alpha \in [\alpha_0,2]$ for some $\alpha_0>0$. In addition, we estimate the difference between the heat kernels…

Let (Z n) n$\ge$0 with Z n = (Z n (i, j)) 1$\le$i,j$\le$p be a p multi-type critical branching process in random environment, and let M n be the expectation of Z n given a fixed environment. We prove theorems on convergence in distribution…

We consider the Riemannian random wave model of Gaussian linear combinations of Laplace eigenfunctions on a general compact Riemannian manifold. With probability one with respect to the Gaussian coefficients, we establish that, both for…

We consider general Markov processes with absorption and provide criteria ensuring the exponential convergence in total variation of the distribution of the process conditioned not to be absorbed. The first one is based on two-sided…

Fix $\nu>0$, denote by $G(\nu/2)$ a Gamma random variable with parameter $\nu/2$ and let $n\geq2$ be a fixed even integer. Consider a sequence $\{F_k\}_{k\geq1}$ of square integrable random variables belonging to the $n$th Wiener chaos of a…

We prove a local central limit theorem (LCLT) for the number of points $N(J)$ in a region $J$ in $\mathbb R^d$ specified by a determinantal point process with an Hermitian kernel. The only assumption is that the variance of $N(J)$ tends to…

Given a strict partial order $\Delta$ on a set $\Lambda$ and an arbitrary ring $R$ with $1\neq 0$, the corresponding McLain group $M(\Delta)$ has been studied in depth. We construct a larger family of McLain groups $G(\Delta)$, where…

We prove some invariance principles for processes which generalize FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution. The limiting processes are extensions of the fractional L\'evy…

When the underlying random variables are Gaussian, the classical Central Limit Theorem (CLT) is trivial, but the functional CLT is not. The objective of the paper is to investigate the functional CLT for stationary Gaussian processes in the…

Fluctuations of the order parameters of the Gardner model for any $\alpha<\alpha_c$ are studied. It is proved that they converge in distribution to a family of jointly Gaussian random variables.

Yor's generalized meander is a temporally inhomogeneous modification of the $2(\nu+1)$-dimensional Bessel process with $\nu > -1$, in which the inhomogeneity is indexed by $\kappa \in [0, 2(\nu+1))$. We introduce the non-colliding particle…

We derive a systematic, multiple time-scale perturbation expansion for the work distribution in isothermal quasi-static Langevin processes. To first order we find a Gaussian distribution reproducing the result of Speck and Seifert [Phys.…

There is a well understood way of generating random coverings of a fixed manifold by sampling homomorphisms from the fundamental group of this manifold into the symmetric group. We prove a central limit theorem for the number of connected…

Let $G$ be a group with a non-elementary action on a proper CAT(0) space $X$, and let $\mu$ be a measure on $G$ such that the random walk $(Z_n)_n$ generated by $\mu$ has finite second moment on $X$. Let $o$ be a basepoint in $X$, and…

The aim of this paper is to give a precise asymptotic description of some eigenvalue statistics stemming from random matrix theory. More precisely, we consider random determinants of the GUE, Laguerre, Uniform Gram and Jacobi beta ensembles…

Given a Coxeter system of large type we prove a non--commutative central limit theorem: After normalisation with the square root of n the characteristic function of the set of the first n generators tends in distribution to Wigners…