Related papers: Large deviation principle for random matrix produc…
We consider the moment space $\mathcal{M}_n^{K}$ corresponding to $p \times p$ complex matrix measures defined on $K$ ($K=[0,1]$ or $K=\D$). We endow this set with the uniform law. We are mainly interested in large deviations principles…
We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation.
We consider a family of positive operator valued measures associated with representations of compact connected Lie groups. For many independent copies of a single state and a tensor power representation we show that the observed probability…
Consider an nxn random matrix X with i.i.d. nonnegative entries with bounded density, mean m, and finite positive variance sigma^2. Let M be the nxn random Markov matrix with i.i.d. rows obtained from X by dividing each row of X by its sum.…
A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…
We prove a large-deviation principle (LDP) for the sample paths of jump Markov processes in the small noise limit when, possibly, all the jump rates vanish uniformly, but slowly enough, in a region of the state space. We further discuss the…
The Whittaker 2d growth model is a triangular continuous Markov diffusion process that appears in many scientific contexts. It has been theoretically intriguing to establish a large deviation principle for this 2d process with a scaling…
Large deviation principles and related results are given for a class of Markov chains associated to the "leaves" in random recursive trees and preferential attachment random graphs, as well as the "cherries" in Yule trees. In particular,…
The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations…
From a suitable integral representation of the Laplace transform of a positive semi-definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for…
This article gives an overview of the emerging literature on large deviations for random graphs. Written for the general mathematical audience, the article begins with a short introduction to the theory of large deviations. This is followed…
We derive a large deviation principle for the empirical measure of zeros of random polynomials with i.i.d. exponential coefficients.
The empirical mean of $n$ independent and identically distributed (i.i.d.) random variables $(X_1,\dots,X_n)$ can be viewed as a suitably normalized scalar projection of the $n$-dimensional random vector $X^{(n)}\doteq(X_1,\dots,X_n)$ in…
We show an extension of Sanov's theorem on large deviations, controlling the tail probabilities of i.i.d. random variables with matching concentration and anti-concentration bounds. This result has a general scope, applies to samples of any…
We derive analytic expressions for infinite products of random 2x2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the…
We consider discrete time Markov chains with Polish state space. The large deviations principle for empirical measures of a Markov chain can equivalently be stated in Laplace principle form, which builds on the convex dual pair of relative…
The large deviations principles are established for a class of multidimensional degenerate stochastic differential equations with reflecting boundary conditions. The results include two cases where the initial conditions are adapted and…
This work concerns generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. First of all, we establish the large deviation principle for forward stochastic differential…
A large deviation principle is established for a general class of stochastic flows in the small noise limit. This result is then applied to a Bayesian formulation of an image matching problem, and an approximate maximum likelihood property…
The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…