Related papers: Large deviations for correlated random variables d…
The goal of this paper is to obtain expectation bounds for the deviation of large sample autocovariance matrices from their means under weak data dependence. While the accuracy of covariance matrix estimation corresponding to independent…
We establish large deviation principles for the largest eigenvalue of large random matrices with variance profiles. For $N \in \mathbb N$, we consider random $N \times N$ symmetric matrices $H^N$ which are such that…
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,…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
We study the probability distribution $P$ of the sum of a large number of non-identically distributed random variables $n_m$. Condensation of fluctuations, the phenomenon whereby one of such variables provides a macroscopic contribution to…
In this paper we study the large deviation behavior of sums of i.i.d. random variables X_i defined on a supercritical Galton-Watson process Z. We assume the finiteness of the moments EX_1^2 and EZ_1log Z_1. The underlying interplay of the…
We derive the distribution of the eigenvalues of a large sample covariance matrix when the data is dependent in time. More precisely, the dependence for each variable $i=1,...,p$ is modelled as a linear process…
We construct a family of chaotic dynamical systems with explicit broad distributions, which always violate the central limit theorem. In particular, we show that the superposition of many statistically independent, identically distributed…
Multivariate statistical analysis is concerned with observations on several variables which are thought to possess some degree of inter-dependence. Driven by problems in genetics and the social sciences, it first flowered in the earlier…
We study general random dynamical systems of continuous maps on some compact metric space. Assuming a local contraction condition and uniqueness of the stationary measure, we establish probabilistic limit laws such as the central limit…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
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…
We calculate the large deviations for the length of the longest alternating subsequence and for the length of the longest increasing subsequence in a uniformly random permutation that avoids a pattern of length three. We treat all six…
We consider the extreme value statistics of correlated random variables that arise from a Langevin equation. Recently, it was shown that the extreme values of the Ornstein-Uhlenbeck process follow a different distribution than those…
We present a large deviation property for the pattern statistics representing the number of occurrences of a symbol in words of given length generated at random according to a rational stochastic model. The result is obtained assuming that…
Suppose X is a random vector, that is distributed uniformly in some n-dimensional convex set. It was conjectured that when the dimension n is very large, there exists a non-zero vector u, such that the distribution of the real random…
We derive a large deviation principle for families of random variables in the basin of attraction of spectrally positive stable distributions by proving a uniform version of the Tauberian theorem for Laplace-Stieltjes transforms. The main…
Large deviations in chaotic dynamics have potentially significant and dramatic consequences. We study large deviations of series of finite lengths $N$ generated by chaotic maps. The distributions generally display an exponential decay with…
In this short note, we study the behaviour of a product of matrices with a simultaneous renormalization. Namely, for any sequence $(A\_n)\_{n\in \mathbb{N}}$ of $d\times d$ complex matrices whose mean $A$ exists and whose norms' means are…
We define a product of algebraic probability spaces equipped with two states. This product is called a conditionally monotone product. This product is a new example of independence in non-commutative probability theory and unifies the…