Large deviations for the occupation times of independent particle systems. (English) Zbl 0864.60076

Summary: We prove a large deviation principle for the density field of independent particle systems in an infinite volume. We then deduce from the one-dimensional case of this result the large deviations for the occupation times of various sets (from microscopic to macroscopic scales) and we recover the theorem established by J. T. Cox and D. Griffeath [Z. Wahrscheinlichkeitstheorie Verw. Geb. 66, 543-558 (1984; Zbl 0551.60028)]. An expression of the rate function is given using the Brownian motion local time as by J.-D. Deuschel and K. Wang [Stochastic Processes Appl. 52, No. 2, 183-209 (1994; Zbl 0813.60029)].


60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F10 Large deviations
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