相关论文: Large deviations and path properties of the true s…

We establish a large deviation principle for the trajectories of Wiener processes subject to random resets to the origin occurring according to a Poisson process. In addition to the pathwise large deviation principle, we identify the rate…

We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…

We study an active random walker model in which a particle's motion is determined by a self-generated field. The field encodes information about the particle's path history. This leads to either self-attractive or self-repelling behavior.…

The dynamical discrete web is a system of one-dimensional coalescing random walks that evolves in an extra dynamical time parameter. At any deterministic dynamical time, the paths behave as coalescing simple symmetric random walks. This…

We study the large deviations of time-integrated observables of Markov diffusions that have perfectly reflecting boundaries. We discuss how the standard spectral approach to dynamical large deviations must be modified to account for such…

In the present work we study self-interacting diffusions following an infinite dimensional approach. First we prove existence and uniqueness of a solution with Markov property. Then we study the corresponding transition semigroup and, more…

Large deviation theory offers a powerful and general statistical framework to study the asymptotic dynamical properties of rare events. The application of the formalism to concrete experimental situations is, however, often restricted by…

We consider a sequence of processes defined on half-line for all non negative t. We give sufficient conditions for Large Deviation Principle (LDP) to hold in the space of continuous functions with a new metric that is more sensitive to…

The large deviation properties of equilibrium (reversible) lattice gases are mathematically reasonably well understood. Much less is known in non--equilibrium, namely for non reversible systems. In this paper we consider a simple example of…

We study a system of N particles with logarithmic, Coulomb or Riesz pairwise interactions, confined by an external potential. We examine a microscopic quantity, the tagged empirical field, for which we prove a large deviation principle at…

We consider a system of $N^{d}$ spins in random environment with a random local mean field type interaction. Each spin has a fixed spatial position on the torus $\mathbb{T}^{d}$, an attached random environment and a spin value in…

We consider self-avoiding walk on finite graphs with large girth. We study a few aspects of the model originally considered by Lawler, Schramm and Werner on finite balls in Z^d. The expected length of a random self avoiding path is…

We establish large deviation principles (LDPs) for empirical measures associated with a sequence of Gibbs distributions on $n$-particle configurations, each of which is defined in terms of an inverse temperature $% \beta_n$ and an energy…

We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…

We prove a Large Deviations Principle for the number of intersections of two independent infinite-time ranges in dimension five and more, improving upon the moment bounds of Khanin, Mazel, Shlosman and Sina{\"i} [KMSS94]. This settles, in…

We give a new proof of the large deviation principle from the hydrodynamic limit for the Ginzberg-Landau model studied in Donsker and Varadhan (1989) using techniques from the theory of stochastic control and weak convergence methods. The…

A global picture of a random particle movement is given by the convex hull of the visited points. We obtained numerically the probability distributions of the volume and surface of the convex hulls of a selection of three types of…

We consider the branching random walk drifting to $-\infty$ and we investigate large deviations-type estimates for the first passage time. We prove the corresponding law of large numbers and the central limit theorem.

We study a class of self-repelling diffusions on compact Riemannian manifolds whose drift is the gradient of a potential accumulated along their trajectory. When the interaction potential admits a suitable spectral decomposition, 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…