Related papers: Temporal Central Limit Theorem for Multidimensiona…

We prove a non-asymptotic central limit theorem for vector-valued martingale differences using Stein's method, and use Poisson's equation to extend the result to functions of Markov Chains. We then show that these results can be applied to…

We consider a counting problem in the setting of hyperbolic dynamics. Let $\phi_t : \Lambda \to \Lambda$ be a weak mixing hyperbolic flow. We count the proportion of prime periodic orbits of $\phi_t$, with length less than $T$, that satisfy…

We prove a central limit theorem for $\log|\zeta(1/2+it)|$ with respect to the measure $|\zeta^{(m)}(1/2+it)|^{2k}dt$ ($k,m\in\mathbb N$), assuming RH and the asymptotic formula for twisted and shifted integral moments of zeta. Under the…

We prove a central limit theorem for a certain class of functions on sparse rank-one inhomogeneous random graphs endowed with additional i.i.d. edge and vertex weights. Our proof of the central limit theorem uses a perturbative form of…

We prove local central limit theorems for partial sums of the form \newline $\,S_n=\sum_{j=0}^{n-1}f_j\circ T_{j-1}\circ\cdots\circ T_1\circ T_0$ where $f_j$ are uniformly H\"older functions and $T_j$ are expanding maps. Using a symbolic…

In this paper, we prove a multivariate central limit theorem for $\ell_q$-norms of high-dimensional random vectors that are chosen uniformly at random in an $\ell_p^n$-ball. As a consequence, we provide several applications on the…

The standard central limit theorem plays a fundamental role in Boltzmann-Gibbs statistical mechanics. This important physical theory has been generalized \cite{Tsallis1988} in 1988 by using the entropy $S_q = \frac{1-\sum_i p_i^q}{q-1}$…

Let $p\geq 3$ be a prime and $n\geq 1$ be an integer. Let $K\subseteq {\mathbb{F}_p}$ denote a fixed subset with $0\in K$. Let $A\subseteq ({\mathbb{F}_p})^n$ be an arbitrary subset such that $$\{…

In this paper we prove that inf_{|z_k| => 1} max_{v=1,...,n^2} |sum_{k=1}^n z_k^v| = sqrt n+O(n^{0.2625+epsilon}). This improves on the bound O(sqrt (n log n)) of Erdos and Renyi. In the special case of $n+1$ being a prime we have…

Consider Jacobi random matrix ensembles with the distributions $$c_{k_1,k_2,k_3}\prod_{1\leq i< j \leq N}\left(x_j-x_i\right)^{k_3}\prod_{i=1}^N…

Let $B=(B_x)_{x\in\mathbb{R}^d}$ be a collection of $N(0,1)$ random variables forming a real-valued continuous stationary Gaussian field on $\mathbb{R}^d$, and set $C(x-y)=\mathbb{E}[B_xB_y]$. Let $\varphi:\mathbb{R}\to\mathbb{R}$ be such…

We investigate here the behaviour of a large typical meandric system, proving a central limit theorem for the number of components of given shape. Our main tool is a theorem of Gao and Wormald, that allows us to deduce a central limit…

In this paper we consider a dynamic Erd\H{o}s-R\'{e}nyi random graph with independent identically distributed edge processes. Our aim is to describe the joint evolution of the entries of a subgraph count vector. The main result of this…

The asymptotics of the first rows and columns of random Young diagrams corresponding to extremal characters of the infinite symmetric group is studied. We consider rows and columns with linear growth in $n$, the number of boxes of random…

This paper deals with the numerical approximation of normalizing constants produced by particle methods, in the general framework of Feynman-Kac sequences of measures. It is well-known that the corresponding estimates satisfy a central…

The theorem of Shannon-McMillan-Breiman states that for every generating partition on an ergodic system, the exponential decay rate of the measure of cylinder sets equals the metric entropy almost everywhere (provided the entropy is…

We establish a new functional central limit theorem result for non-invertible measure preserving maps that are not necessarily ergodic, using the Perron-Frobenius operator. We apply the result to asymptotically periodic transformations and…

Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a $d$-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are…

The purpose of this note is to establish a Central Limit Theorem for the number of eigenvalues of a Wigner matrix in an interval. The proof relies on the correct aymptotics of the variance of the eigenvalue counting function of GUE matrices…

Dobrushin and Tirozzi [14] showed that, for a Gibbs measure with the finite-range potential, the Local Central Limit Theorem is implied by the Integral Central Limit Theorem. Campanino, Capocaccia, and Tirozzi [7] extended this result for a…