Related papers: Large deviations principle for terminating multidi…
Let $X$ be a L\'evy process with regularly varying L\'evy measure $\nu$. We obtain sample-path large deviations for scaled processes $\bar X_n(t) \triangleq X(nt)/n$ and obtain a similar result for random walks. Our results yield detailed…
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 prove a large deviations principle for the empirical measures of a class of biorthogonal and multiple orthogonal polynomial ensembles that includes biorthogonal Laguerre, Jacobi and Hermite ensembles, the matrix model of Lueck, Sommers…
Much work in the study of large deviations for random graph models is focused on the dense regime where the theory of graphons has emerged as a principal tool. These tools do not give a good approach to large deviation problems for random…
We give an explicit formula for the most likely path to extinction for the Galton-Watson processes with large initial population. We establish this result with the help of the large deviation principle (LDP) which also recovers the…
We study the totally asymmetric exclusion process on the positive integers with a single particle source at the origin. Liggett (1975) has shown that the long term behaviour of this process has a phase transition: If the particle production…
We prove a law of large numbers in terms of complete convergence of independent random variables taking values in increments of monotone functions, with convergence uniform both in the initial and the final time. The result holds also for…
We study the large deviations principle (LDP) for stationary solutions of a class of stochastic differential equations (SDE) in infinite time intervals by the weak convergence approach, and then establish the LDP for the invariant measures…
Large deviation theory is a branch of probability theory that is devoted to a study of the "rate" at which empirical estimates of various quantities converge to their true values. The object of study in this paper is the rate at which…
Cumulative probability models (CPMs) are a robust alternative to linear models for continuous outcomes. However, they are not feasible for very large datasets due to elevated running time and memory usage, which depend on the sample size,…
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…
We prove a large deviation principle for the point process of large Poisson $k$-nearest neighbor balls in hyperbolic space. More precisely, we consider a stationary Poisson point process of unit intensity in a growing sampling window in…
We prove the Large Deviation Principle for the empirical process in a system of locally interacting Brownian motions in the nonequilibrium dynamic. Such a phenomenon has been proven only for two lattice systems: the symmetric simple…
In this paper we prove a Large Deviation Principle for the sequence of symmetrised empirical measures $\frac{1}{n} \sum_{i=1}^{n} \delta_{(X^n_i,X^n_{\sigma_n(i)})}$ where $\sigma_n$ is a random permutation and $((X_i^n)_{1 \leq i \leq…
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…
We prove a {\it{quenched}} large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on $\mathbb Z^d$ ($d\geq 2$). The models under interest include classical Bernoulli bond and site percolation…
The aim of this paper is to investigate the large deviations for a class of slow-fast mean-field diffusions, which extends some existing results to the case where the laws of fast process are also involved in the slow component. Due to the…
In this paper we produce precise large deviation estimates through the lens of mod-Poisson convergence. We apply a general result to various examples from number theory, Dedekind domains and polynomials over finite fields when an element is…
In this article we establish a large deviation principle for the empirical measures of a simple spatially inhomogeneous random walk on $\overline{\mathbb{Z}}$, the two-point compactification of $\mathbb{Z}$. The classical Donsker--Varadhan…
We combine hydrodynamic and modulated energy techniques to study the large deviations of systems of particles with pairwise singular repulsive interactions and additive noise. Specifically, we examine periodic Riesz interactions indexed by…