Related papers: Large Deviations in the Supremum Norm for a Reacti…
Birth-death processes form a natural class where ideas and results on large deviations can be tested. In this paper, we derive a large deviation principle under the assumption that the rate of a jump down (death) is growing asymptotically…
We consider real-valued branching random walks and prove a large deviation result for the position of the rightmost particle. The position of the rightmost particle is the maximum of a collection of a random number of dependent random…
We study numerically the distributions of the length $L$ of the longest increasing subsequence (LIS) for the two cases of random permutations and of one-dimensional random walks. Using sophisticated large-deviation algorithms, we are able…
We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…
We prove existence of the large deviation principle, with a proper convex rate function, for the distribution of the renormalized distance from the origin of a random walk on a free product of finitely generated groups. As a consequence, we…
We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…
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…
A large deviation principle is established for a two-scale stochastic system in which the slow component is a continuous process given by a small noise finite dimensional It\^{o} stochastic differential equation, and the fast component is a…
We consider the precise upper large deviations estimates for the maximal displacement of a branching random walk. In addition, we obtain a description of the extremal process of the branching random walk conditioned on this large deviations…
In this paper we present a new and flexible method to show that, in one dimension, various self-repellent random walks converge to self-repellent Brownian motion in the limit of weak interaction after appropriate space-time scaling. Our…
High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…
In biological, glassy, and active systems, various tracers exhibit Laplace-like, i.e., exponential, spreading of the diffusing packet of particles. The limitations of the central limit theorem in fully capturing the behaviors of such…
We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation principle is…
We consider a jump-diffusion process on a bounded domain with reflection at the boundary, and establish long-term results for a general additive process of its path. This includes the long-term behaviour of its occupation time in the…
We study a system of hard rods of finite size in one space dimension, which move by Brownian noise while avoiding overlap. We consider a scaling in which the number of particles tends to infinity while the volume fraction of the rods…
Recently observation of random walks in complex environments like the cell and other glassy systems revealed that the spreading of particles, at its tails, follows a spatial exponential decay instead of the canonical Gaussian. We use the…
In this paper we consider the multispecies stirring process on the discrete torus. We prove a large deviation principle for the trajectory of the vector of densities of the different species. The technique of proof consists in extending the…
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
We study the scaling limits of stochastic gradient descent (SGD) with constant step-size in the high-dimensional regime. We prove limit theorems for the trajectories of summary statistics (i.e., finite-dimensional functions) of SGD as the…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…