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Space‐time large deviations for interacting particle systems
Author(s) -
Pra P. Dai
Publication year - 1993
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160460305
Subject(s) - rate function , large deviations theory , particle system , mathematics , interacting particle system , statistical physics , markov chain , markov process , range (aeronautics) , mathematical analysis , stochastic differential equation , physics , computer science , statistics , continuous time stochastic process , operating system , materials science , composite material
We prove a process‐level large deviation principle for the space‐time empirical averages of continuous‐time systems on an infinite lattice. Our methods rely on the Donsker‐Varadhan large deviation theory for Markov processes, and allow us to express the rate function rather explicitly in terms of the Markov generator of the infinite particle system. We can prove our principle for a large class of spin systems with no particle exchange, as well as for infinite diffusion processes whose drift is the gradient of a finite range Hamiltonian. © 1993 John Wiley & Sons, Inc.