Related papers: Self-interacting diffusions IV: Rate of convergenc…
The aim of the paper is to establish a large deviation principle (LDP) for the empirical measure of mean-field interacting diffusions in a random environment. The point is to derive such a result once the environment has been frozen…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…
We study diffusive mixing in the presence of thermal fluctuations under the assumption of large Schmidt number. In this regime we obtain a limiting equation that contains a diffusive thermal drift term with diffusion coefficient obeying a…
We consider processes that coincide with a given diffusion process outside a finite collection of domains. In each of the domains, there is, additionally, a large drift directed towards the interior of the domain. We describe the limiting…
We consider a mean-field system of path-dependent stochastic interacting diffusions in random media over a finite time window. The interaction term is given as a function of the empirical measure and is allowed to be non-linear and path…
We present a unified approach to characterising fast-reaction limits of systems of either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary differential equation, on unbounded domains, motivated by models…
A stochastic dynamics $({\bf X}(t))_{t\ge0}$ of a classical continuous system is a stochastic process which takes values in the space $\Gamma$ of all locally finite subsets (configurations) in $\Bbb R$ and which has a Gibbs measure $\mu$ as…
This paper investigates the dynamics of a reaction-diffusion system with two free boundaries, modeling the invasion of two cooperative species, where the free boundaries represent expanding fronts. We first analyze the long-term behavior of…
For many stochastic diffusion processes with mean field interaction, convergence of the rescaled total mass processes towards a diffusion process is known. Here we show convergence of the so-called finite system scheme for interacting…
We describe the construction of a conserved reaction-diffusion system that exhibits self-organized critical (avalanche-like) behavior under the action of a slow addition of particles. The model provides an illustration of the general…
We consider the drift and diffusion properties of periodically driven renewal processes. These processes are defined by a periodically time dependent waiting time distribution, which governs the interval between subsequent events. We show…
Let M be a compact connected oriented Riemannian manifold. The purpose of this paper is to investigate the long time behavior of a degenerate stochastic differential equation on the state space $M\times \mathbb{R}^{n}$; which is obtained…
We consider asymptotic problems concerning the motion of interface separating the regions of large and small values of the solution of a reaction-diffusion equation in the media consisting of domains with different characteristics…
The diffusion properties of self-propelled particles which move at constant speed and, in addition, reverse their direction of motion repeatedly are investigated. The internal dynamics of particles triggering these reversal processes is…
Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…
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…
We provide an explicit rigorous derivation of a diffusion limit - a stochastic differential equation with additive noise - from a deterministic skew-product flow. This flow is assumed to exhibit time-scale separation and has the form of a…
We consider extended slow-fast systems of N interacting diffusions. The typical behavior of the empirical density is described by a nonlinear McKean-Vlasov equation depending on , the scaling parameter separating the time scale of the slow…
In this work, we focus on the behavior of a single passive Brownian particle in a suspension of passive particles with short-range repulsive interactions and a larger self-diffusion coefficient. While the forces affecting the…