Uniform Convergence in some Limit Theorems for Multiple Particle Systems

For n particles di using throughout R or Rd let n t A A B t be the random measure that counts the number of particles in A at time t It is shown 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 M C L R g n 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 Research supported in part by National Science Foundation grant DMS Research supported in part by National Science Foundation grant DMS and the University of Connecticut Research Foundation AMS subject classi cations Primary F F secondary J J