Related papers: A Law Limit Theorem for a sequence of random varia…

Let $\{Z_{m},m\geq 0\}$ be a critical branching process in random environment and $\{S_{m},m\geq 0\}$ be its associated random walk. Assuming that the increments distribution of the associated random walk belongs without centering to the…

We establish a central limit theorem for tensor product random variables $c_k:=a_k \otimes a_k$, where $(a_k)_{k \in \mathbb{N}}$ is a free family of variables. We show that if the variables $a_k$ are centered, the limiting law is the…

We find the limit distributions for a spectrum of a system of n particles governed by a k-body interaction. The hamiltonian of this system is modelled by a Gaussian random matrix. We show that the limit distribution is a q-deformed Gaussian…

We introduce and study the r-Lah distribution whose definition involves r-Stirling numbers of both kinds. We compute its expectation and variance, show its log-concavity and prove limit theorems for this distribution. We use these results…

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…

The limit behavior is studied for the distributions of normalized U- and V-statistics of an arbitrary order with canonical (degenerate) kernels, based on samples of increasing sizes from a stationary sequence of observations satisfying…

The Lyapunov spectra of random U(1) extensions of expanding maps on the torus were investigated in our previous work [NW2015]. Using the result, we extend the recent spectral approach for quenched limit theorems for expanding maps…

We consider arbitrary discrete probability laws on the real line. We obtain a criterion of their belonging to a new class of quasi-infinitely divisible laws, which is a wide natural extension of the class of well known infinitely divisible…

This paper provides a quantitative version of de Finetti law of large numbers. Given an infinite sequence $\{X_n\}_{n \geq 1}$ of exchangeable Bernoulli variables, it is well-known that $\frac{1}{n} \sum_{i = 1}^n X_i…

We obtain a strong invariance principle for nonconventional sums and applying this result we derive for them a version of the law of iterated logarithm, as well as an almost sure central limit theorem. Among motivations for such results are…

Euler integrals of deterministic functions have recently been shown to have a wide variety of possible applications, including in signal processing, data aggregation and network sensing. Adding random noise to these scenarios, as is natural…

We consider an indexed class of real symmetric random matrices which generalize the symmetric Hankel and Reverse Circulant matrices. We show that the limiting spectral distributions of these matrices exist almost surely and the limit is…

We give a complete expansion, at any accuracy order, for the iterated convolution of a complex valued integrable sequence in one space dimension. The remainders are estimated sharply with generalized Gaussian bounds. The result applies in…

We consider the adjacency matrix $A$ of a large random graph and study fluctuations of the function $f_n(z,u)=\frac{1}{n}\sum_{k=1}^n\exp\{-uG_{kk}(z)\}$ with $G(z)=(z-iA)^{-1}$. We prove that the moments of fluctuations normalized by…

We establish general "collapse to the mean" principles that provide conditions under which a law-invariant functional reduces to an expectation. In the convex setting, we retrieve and sharpen known results from the literature. However, our…

In statistical problems, a set of parameterized probability distributions is used to estimate the true probability distribution. If Fisher information matrix at the true distribution is singular, then it has been left unknown what we can…

Let $(X_n)_{n\in \mathbb{N}}$ be a sequence of i.i.d. random variables with distribution $\mathbb P(X_1=1)=\mathbb P(X_1=-1)=1/2$. Let $F(\sigma)=\sum_{n=1}^\infty X_nn^{-\sigma}$. We prove that the following holds almost surely…

We investigate the spectrum of the infinitesimal generator of the continuous time random walk on a randomly weighted oriented graph. This is the non-Hermitian random nxn matrix L defined by L(j,k)=X(j,k) if k<>j and…

In this paper is proved the limit theorem for randomly indexed sequence of random processes in the case where sequences of random index and random processes are independent, also the estimation of convergence rate is obtained.

U-max statistics were introduced by Lao and Mayer in 2008. Instead of averaging the kernel over all possible subsets of the original sample, they considered the maximum of the kernel. Such statistics are natural in stochastic geometry.…