Infinite interacting diffusion particles I: Equilibrium process and its scaling limit

2 5 N ov 2 00 3 Infinite interacting diffusion particles I : Equilibrium process and its scaling limit

A stochastic dynamics (X(t))t≥0 of a classical continuous system is a stochastic process which takes values in the space Γ of all locally finite subsets (configurations) in R and which has a Gibbs measure μ as an invariant measure. We assume that μ corresponds to a symmetric pair potential φ(x − y). An important class of stochastic dynamics of a classical continuous system is formed by diffusio...

Mean field limit for interacting particles

Birth, death and diffusion of interacting particles

Individual-based models of chemical or biological dynamics usually consider individual entities diffusing in space and performing a birth-death type dynamics. In this work we study the properties of a model in this class where the birth dynamics is mediated by the local, within a given distance, density of particles. Groups of individuals are formed in the system and in this paper we concentrat...

Zero Temperature Limit for Interacting Brownian Particles

We consider a system of interacting Brownian particles in R with a pairwise potential, which is radially symmetric, of finite range and attains a unique minimum when the distance of two particles becomes a > 0. The asymptotic behavior of the system is studied under the zero temperature limit from both microscopic and macroscopic aspects. If the system is rigidly crystallized, namely if the part...

Diffusion of interacting Brownian particles: Jamming and anomalous diffusion.

The free self-diffusion of an assembly of interacting particles confined on a quasi-one-dimensional ring is investigated both numerically and analytically. The interparticle pairwise interaction can be either attractive or repulsive and the energy barrier opposing thermal hopping of two particles one past the other is finite. Thus, for sufficiently long times, self-diffusion becomes normal or c...