Di usive clustering of interacting Brownian motions on Z 2
نویسنده
چکیده
In this paper we investigate the cluster behavior of linearly interacting Brownian motions indexed by Z. We show that (on a logarithmic scale) the block average process converges in path space to Brownian motion. c © 2000 Elsevier Science B.V. All rights reserved. MSC: primary 60K35; secondary 60G15; 60F17
منابع مشابه
Motion In A Gaussian , Incompressible Flow
We prove that the solution of a system of random ordinary di erential equations dX(t) dt = V(t;X(t)) with di usive scaling, X"(t) = "X( t " ), converges weakly to a Brownian Motion when " # 0. We assume that V(t;x), t 2 R, x 2 R is a d-dimensional, random, incompressible, stationary Gaussian eld which has mean zero and decorrelates in nite time.
متن کاملar X iv : 0 90 5 . 39 73 v 1 [ m at h . PR ] 2 5 M ay 2 00 9 Tagged particle processes and their non - explosion criteria
We give a derivation of tagged particle processes from unlabeled interacting Brownian motions. We give a criteria of the non-explosion property of tagged particle processes. We prove the quasi-regularity of Dirichlet forms describing the environment seen from the tagged particle, which were used in previous papers to prove the invariance principle of tagged particles of interacting Brownian mot...
متن کاملLimit Theorems for Tagged Particles ∗
We review old and new results about the limiting behaviour of a tagged particle in different interacting particle systems: (a) independent particles with no mass in one dimension with continuous paths like Brownian motions and ideal gases; (b) reversible processes on R d or Z d like interacting Brownian motions and Kawasaki dynamics; (c) simple exclusion processes; (d) zero range processes; (e)...
متن کاملInteracting Brownian motions and the Gross-Pitaevskii formula
We review probabilistic approaches to the Gross-Pitaevskii theory describing interacting dilute systems of particles. The main achievement are large deviations principles for the mean occupation measure of a large system of interacting Brownian motions in a trapping potential. The corresponding rate functions are given as variational problems whose solution provide effective descriptions of the...
متن کاملInteracting Brownian motions in infinite dimensions with logarithmic interaction potentials
We investigate the construction of diffusions consisting of infinitely numerous Brownian particles moving in R and interacting via logarithmic functions (2D Coulomb potentials). These potentials are really strong and long range in nature. The associated equilibrium states are no longer Gibbs measures. We present general results for the construction of such diffusions and, as applications thereo...
متن کامل