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Benois, O.

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

Ann. Appl. Probab. 6, No. 1, 269-296 (1996).
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)].

Cited in 6 Documents

MSC:

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

Keywords:

occupation times; large deviations; rate functions; infinite particle systems

Citations:

Zbl 0551.60028; Zbl 0813.60029
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\textit{O. Benois}, Ann. Appl. Probab. 6, No. 1, 269--296 (1996; Zbl 0864.60076)
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References:

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