Related papers: Large deviations for zeros of random polynomials w…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
Laws of large numbers, starting from certain nonequilibrium measures, have been shown for the integrated current across a bond, and a tagged particle in one-dimensional symmetric nearest-neighbor simple exclusion [Ann. Inst. Henri Poincare…
This is a survey of some invariances that arise in dynamical systems theory in the presence of zero Lyapunov exponents.
Motivated by problems arising in random sampling of trigonometric polynomials, we derive exponential inequalities for the operator norm of the difference between the sample second moment matrix $n^{-1}U^*U$ and its expectation where $U$ is…
We prove the the large deviation principle(LDP) for the law of the one-dimensional semilinear stochastic partial differential equations driven by nonlinear multiplicative noise. Firstly, combining the energy estimate and approximation…
In this work, we investigate the McKean-Vlasov stochastic partial differential equations driven by Poisson random measure. By adapting the variational framework, we prove the well-posedness and large deviation principle for a class of…
In this article, we obtain upper bounds on the number of irreducible factors of some classes of polynomials having integer coefficients, which in particular yield some of the well known irreducibility criteria. For devising our results, we…
We establish a large deviation principle for the empirical spectral measure of a sample covariance matrix with sub-Gaussian entries, which extends Bordenave and Caputo's result for Wigner matrices having the same type of entries [7]. To…
In this paper we investigate the asymptotic distribution of the zeros of polynomials $P_{n}(x)$ satisfying a first order differential-difference equation. We give several examples of orthogonal and non-orthogonal families.
We prove a large deviation principle for the sequence of push-forwards of empirical measures in the setting of Riesz potential interactions on compact subsets K in R^d with continuous external fields. Our results are valid for base measures…
In this paper we study the Large Deviation Principle (LDP in abbreviation) for a class of Stochastic Partial Differential Equations (SPDEs) in the whole space $\mathbb{R}^d$, with arbitrary dimension $d\geq 1$, under random influence which…
This paper is concerned with the general theme of relating the Large Deviation Principle (LDP) for the invariant measures of stochastic processes to the associated sample path LDP. It is shown that if the sample path deviation function…
We prove a large deviation principle for the point process associated to $k$-element connected components in $\mathbb R^d$ with respect to the connectivity radii $r_n\to\infty$. The random points are generated from a homogeneous Poisson…
The entropy of an ergodic finite-alphabet process can be computed from a single typical sample path x_1^n using the entropy of the k-block empirical probability and letting k grow with $n$ roughly like log n. We further assume that the…
Large and moderate deviation principles are proved for Engel continued fractions, a new type of continued fraction expansion with non-decreasing partial quotients in number theory.
We study the dynamics of smooth interval maps with non-flat critical points. For every such a map that is topologically exact, we establish the full (level-2) Large Deviation Principle for empirical means. In particular, the Large Deviation…
Stochastic partial differential equations driven by Poisson random measures (PRM) have been proposed as models for many different physical systems, where they are viewed as a refinement of a corresponding noiseless partial differential…
Starting with the large deviation principle (LDP) for the Erd\H{o}s-R\'enyi binomial random graph $\mathcal{G}(n,p)$ (edge indicators are i.i.d.), due to Chatterjee and Varadhan (2011), we derive the LDP for the uniform random graph…
This work is concerned with the large deviation principle for a family of slow-fast systems perturbed by infinite-dimensional mixed fractional Brownian motion with Hurst parameter $H\in(\frac12,1)$. We adopt the weak convergence method…
We establish a large deviation principle for the empirical measure process associated with a general class of finite-state mean field interacting particle systems with Lipschitz continuous transition rates that satisfy a certain ergodicity…