Abstract not found

For n particles di using throughout R (or Rd), let n�t(A), A 2B, t 0, be the random measure that counts the number of particles in A at time t. Itisshown that for some basic models (Brownian particles with or without branching and di usion with a simple interaction) the processes f ( n�t ( ) ; E n�t ()) = p n: t 2 [0�M] � 2 CL (R)g, n 2 N, converge in law uniformly in (t �). Previous results consider only convergence in law uniform in t but not in. The methods used are from empirical process theory. 1

Abstract. We examine the fluctuations of the empirical density measure for the colour version of the symmetric nearest neighbour zero range particle systems in dimension one. We show that the weak limit of these fluctuations is the solution of a system of coupled generalized Ornstein-Uhlenbeck processes. We also discuss how this result may be used to prove a central limit theorem for the tagged particle on the level of finite dimensional distributions, and identify the limiting variance. This is the central limit theorem associated to propagation of chaos for this interacting particle system. 1.

Occupation time limits of inhomogeneous Poisson systems of independent particles

We describe all countable particle systems on R which have the following three properties: independence, Gaussianity, and stationarity. More precisely, we consider particles on the real line starting at the points of a Poisson point process with intensity measure m and moving independently of each other according to the law of some Gaussian process ξ. We describe all pairs (m, ξ) generating a stationary particle system, obtaining three families of examples. One of these families appeared in connection with extremes of independent Gaussian processes in [Z. Kabluchko, M. Schlather, L. de Haan, Stationary max-stable fields associated to negative definite functions, Ann. Probab. (2009), in press].