Related papers: Large deviations for the largest eigenvalue of gen…

This work establishes a large deviation principle for the spectral measure of the Lax matrix associated to the periodic Toda chain of $N$ particles, subject to a generalised Gibbs measure. This large deviation principle is governed by a…

We consider the large deviations of the smallest eigenvalue of the Wishart-Laguerre Ensemble. Using the Coulomb gas picture we obtain rate functions for the large fluctuations to the left and the right of the hard edge. Our findings are…

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…

We consider the extreme eigenvalues of the sample covariance matrix $Q=YY^*$ under the generalized elliptical model that $Y=\Sigma^{1/2}XD.$ Here $\Sigma$ is a bounded $p \times p$ positive definite deterministic matrix representing the…

A variational principle for gauge theories of gravity is presented, which maintains manifest covariance under the symmetries to which the action is invariant, throughout the calculation of the equations of motion and conservation laws. This…

We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus…

Let $\mathcal{G}(N,\frac 1Nt_N)$ be the Erd\H{o}s-R\'enyi graph with connection probability $\frac 1Nt_N\sim t/N$ as $N\to\infty$ for a fixed $t\in(0,\infty)$. We derive a large-deviations principle for the empirical measure of the sizes of…

We present two examples of a large deviations principle where the rate function is not strictly convex. This is motivated by a model used in mathematical finance (the Heston model), and adds a new item to the zoology of non strictly convex…

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…

We establish sharp tail asymptotics for component-wise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the…

We introduce a new random matrix model called distance covariance matrix in this paper, whose normalized trace is equivalent to the distance covariance. We first derive a deterministic limit for the eigenvalue distribution of the distance…

The Boltzmann equation is one of the most famous equations and has vast applications in modern science. In the current study, we take the randomness of binary collisions into consideration and generalize the classical Boltzmann equation…

We study sample covariance matrices arising from rectangular random matrices with i.i.d. columns. It was previously known that the resolvent of these matrices admits a deterministic equivalent when the spectral parameter stays bounded away…

Let $G_1,\dots,G_m$ be independent copies of the standard gaussian random vector in $\mathbb{R}^d$. We show that there is an absolute constant $c$ such that for any $A \subset S^{d-1}$, with probability at least $1-2\exp(-c\Delta m)$, for…

This work focuses on multivalued stochastic differential equations with jumps. First, by employing the weak convergence approach, we establish the Freidlin-Wentzell uniform large deviation principle and the Dembo-Zeitouni uniform large…

We study large deviations of the size of the largest connected component in a general class of inhomogeneous random graphs with iid weights, parametrized so that the degree distribution is regularly varying. We derive a large-deviation…

Large-margin classifiers are popular methods for classification. We derive the asymptotic expression for the generalization error of a family of large-margin classifiers in the limit of both sample size $n$ and dimension $p$ going to…

Let $X_1,\dots, X_n$ be independent and identically distributed random vectors in $\mathbb{R}^d$. Suppose $\mathbb{E} X_1=0$, $\mathrm{Cov}(X_1)=I_d$, where $I_d$ is the $d\times d$ identity matrix. Suppose further that there exist positive…

We consider asymptotic distributions of maximum deviations of sample covariance matrices, a fundamental problem in high-dimensional inference of covariances. Under mild dependence conditions on the entries of the data matrices, we establish…

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…