2022/01/25 by Xue, Xiaofeng
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2201.10099
In this paper we are concerned with hydrodynamics of a class of N-urn linear systems, which include voter models, pair-symmetric exclusion processes and binary contact path processes on N urns as special cases. We show that the hydrodynamic limit of our process is driven by a (C[0,1])^′-valued linear ordinary differential equation and the fluctuation of our process, i.e, central limit theorem from the hydrodynamic limit, is driven by a (C[0, 1])^′-valued Ornstein-Uhlenbeck process. To derive above main results, we need several replacement lemmas. An extension in linear systems of Chapman-Kolmogorov equation plays key role in proofs of these replacement lemmas.