Related papers: Large deviations for zeros of random polynomials w…
In this paper, we establish the invariance principle and the large deviation for the biased random walk $RW_{\lambda}$ with $\lambda \in [0,1)$ on $\mathbb{Z}^d, d\geq 1$.
We investigate large deviations for the empirical measure of the position and momentum of a particle traveling in a box with hot walls. The particle travels with uniform speed from left to right, until it hits the right boundary. Then it is…
We consider random trigonometric polynomials with general dependent coefficients. We show that under mild hypotheses on the structure of dependence, the asymptotics as the degree goes to infinity of the expected number of real zeros…
In this note we initiate the probabilistic study of the critical points of polynomials of large degree with a given distribution of roots. Namely, let f be a polynomial of degree n whose zeros are chosen IID from a probability measure mu on…
In this paper, we establish a large deviation principle for the conservative stochastic partial differential equations, whose solutions are related to stochastic differential equations with interaction. The weak convergence method and the…
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they…
We derive a large deviations principle for the two-dimensional two-component plasma in a box. As a consequence, we obtain a variational representation for the free energy, and also show that the macroscopic empirical measure of either…
We prove the large deviations principle (LDP) for the law of the solutions to a class of semilinear stochastic partial differential equations driven by multiplicative noise. Our proof is based on the weak convergence approach and…
In this paper, we establish large deviation principle for the strong solution of a doubly nonlinear PDE driven by small multiplicative Brownian noise. Motononicity arguments and the weak convergence approach have been exploited in the…
We calculate the zeros of an exponential polynomial of some variables by a classical algorithm and quantum algorithms which are based on the method of van Dam and Shparlinski, they treated the case of two variables, and compare with the…
In this paper, we establish the large deviation principle for 3D stochastic primitive equations with small perturbation multiplicative noise. The proof is mainly based on the weak convergence approach.
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…
This paper establishes a Freidlin-Wentzell large deviation principle for stochastic differential equations(SDEs) under locally weak monotonicity conditions and Lyapunov conditions. We illustrate the main result of the paper by showing that…
We evaluate the number of monic polynomials (of arbitrary degree $N$) the zeros of which equal their coefficients when these are allowed to take arbitrary complex values. In the following, we call polynomials with this property {\em…
We study global distribution of zeros for a wide range of ensembles of random polynomials. Two main directions are related to almost sure limits of the zero counting measures, and to quantitative results on the expected number of zeros in…
We study large and moderate deviations for a life insurance portfolio, without assuming identically distributed losses. The crucial assumption is that losses are bounded, and that variances are bounded below. From a standard large…
We demonstrate the large deviation property for the mild solutions of stochastic evolution equations with monotone nonlinearity and multiplica- tive noise. This is achieved using the recently developed weak convergence method, in studying…
A large deviation principle is derived for stochastic partial differential equations with slow-fast components. The result shows that the rate function is exactly that of the averaged equation plus the fluctuating deviation which is a…
We prove a maximal-type large deviation principle for dynamical systems with arbitrarily slow polynomial mixing rates. Also several applications, particularly to billiard systems, are presented.
We establish a large deviation principle for the smallest eigenvalue of a random matrix model composed of the sum of a GOE matrix and a diagonal matrix with an outlier. Our result generalizes and unifies previously studied cases.