Related papers: Point processes and the infinite symmetric group. …
Chi-square processes with trend appear naturally as limiting processes in various statistical models. In this paper we are concerned with the exact tail asymptotics of the supremum taken over (0; 1) of a class of locally stationary…
A class of exact non-renormalized extremal correlators of half-BPS operators in N=4 SYM, with U(N) gauge group, is shown to satisfy finite factorization equations reminiscent of topological gauge theories. The finite factorization equations…
We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one…
In this article we introduce two new perfect simulation algorithms for chains with infinite memory. Both algorithms belong to the coupling of past procedures. The novelty of our approach is that it allows to include unknown states to the…
Representation theory and the theory of symmetric functions have played a central role in Random Matrix Theory in the computation of quantities such as joint moments of traces and joint moments of characteristic polynomials of matrices…
In this paper we propagate a large deviations approach for proving limit theory for (generally) multivariate time series with heavy tails. We make this notion precise by introducing regularly varying time series. We provide general large…
We construct families of rational functions $f \colon \bP^1_k \to \bP^1_k$ of degree $d \geq 2$ over a perfect field $k$ whose associated fixed-point processes fail to be martingales. Conversely, for any normal variety $X \subset…
We present a new semi-classical theory for describing pairing in finite Fermi systems. It is based in taking the $\hbar \to 0$, i.e. Thomas-Fermi, limit of the gap equation written in the basis of the mean field (weak coupling). In addition…
In this research paper, the relationship between finite / countable state space stochastic processes and point processes is explored. Utilizing the known relationship between Poisson processes and continuous time Markov chains, finite /…
Understanding the tail behavior of distributions is crucial in statistical theory. For instance, the tail of a distribution plays a ubiquitous role in extreme value statistics, where it is associated with the likelihood of extreme events.…
A class of stochastic processes strongly related to random sums plays an important role in network and in finance. In this paper we study this kind of stochastic process discuss an overtime unchanged parameter and reveal its asymptotic…
This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the…
In this paper we analyze the covariance kernel of the Gaussian process that arises as the limit of fluctuations of linear spectral statistics for Wigner matrices with a few moments. More precisely, the process we study here corresponds to…
The theory of finite-size scaling explains how the singular behavior of thermodynamic quantities in the critical point of a phase transition emerges when the size of the system becomes infinite. Usually, this theory is presented in a…
We consider the determinantal point process with the confluent hypergeometric kernel. This process is a universal point process in random matrix theory and describes the distribution of eigenvalues of large random Hermitian matrices near…
We give a descriptive review of the Fermionic basis approach to the theory of correlation functions of the XXZ quantum spin chain. The emphasis is on explicit formulae for short-range correlation functions which will be presented in a way…
We provide a new extension of Breiman's Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterization of regular variation on cones in $[0,\infty)^d$…
A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling…
We establish the one-to one bilateral interrelations between an asymptotic behavior for the tail of distributions for random variables and its great moments evaluation. Our results generalize the famous Richter's ones.
Non-Hermitean operators may appear during the calculation of a partition function in various models of statistical mechanics. The tail eigen-states, having anomalously small real part of energy $Re(\eps)$, became naturally important in this…