相关论文: From classical to modern central limit theorems

We establish a central limit theorem for the log-determinant $\log|\det(M_n)|$ of a Wigner matrix $M_n$, under the assumption of four matching moments with either the GUE or GOE ensemble. More specifically, we show that this log-determinant…

We discuss CLT for the global and local linear statistics of random matrices from classical compact groups. The main part of our proofs are certain combinatorial identities much in the spirit of works by Kac and Spohn.

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 $S_q = \frac{1-\sum_i p_i^q}{q-1}$…

A fractional binomial distribution, introduced by Hino and Namba (2024) via the generalized binomial theorem, is a fractional variant of the classical binomial distribution. Building upon previous work that established limit theorems, such…

When the limiting compensator of a sequence of martingales is continuous, we obtain a weak convergence theorem for the martingales; the limiting process can be written as a Brownian motion evaluated at the compensator and we find sufficient…

Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point…

This is a translation of Harald Cram\'er's article, 'On a new limit theorem in probability theory', published in French in 1938 and deriving what is considered by mathematicians to be the first large deviation result. My hope is that this…

We investigate in this paper the distribution of the discrepancy of various lattice counting functions. In particular, we prove that the number of lattice points contained in certain domains defined by products of linear forms satisfies a…

A self-consistent thermodynamic framework is presented for power-law canonical distributions based on the generalized central limit theorem by extending the discussion given by Khinchin for deriving Gibbsian canonical ensemble theory. The…

In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal…

We obtain large deviations estimates for both sequential and random compositions of intermittent maps. We also address the question of whether or not centering is necessary for the quenched central limit theorems (CLT) obtained by Nicol,…

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…

We check claims for a generalized central limit theorem holding at the Feigenbaum (infinite bifurcation) point of the logistic map, made recently by U. Tirnakli, C. Beck, and C. Tsallis (Phys. Rev. {\bf 75}, 040106(R) (2007)). We show that…

Considerable thought has been devoted to an adequate definition of the class of infinite, random binary sequences (the sort of sequence that almost certainly arises from flipping a fair coin indefinitely). The first mathematical exploration…

The Central Sets Theorem near zero was originally proved by Hindman and Leader. Later a version of Central Sets Theorem was proved by De, Hindman and Strauss known to be the stronger Central Sets Theorem. Subsequently many other versions of…

In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems…

An essential character for a distribution to play a central role in the limit theory is infinite divisibility. In this note, we prove that the Conway-Maxwell-Poisson (CMP) distribution is infinitely divisible iff it is the Poisson or…

The central limit for the product of free random variables are studied by evaluating all the moments of the limit distribution. The logarithm of the central limit is found to be the same as the sum of two independent free random variables:…

We prove a central limit theorem with aassumptions which are many weak than classical conditions

The Conway-Maxwell-Poisson (CMP) distribution is a natural two-parameter generalisation of the Poisson distribution which has received some attention in the statistics literature in recent years by offering flexible generalisations of some…