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Large deviations and law of large numbers for a mean field type interacting particle systems

Author

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  • Léonard, C.

Abstract

In this paper, we are interested in the behaviour of the empirical measure of a large exchangeable system of N interacting particles living in a Polish space S, whose law in SN is the Gibbs measure given at 0.1. We get a Sanov type result for the large deviations of the empirical measure, and a weak law of large numbers, as N tends to infinity. Both handle the case of phase coexistence. A strong law of large numbers is obtained when the infinite system has a unique phase. All these convergences take place in a subspace of the probability measures whose topology is at least stronger than the usual weak one.

Suggested Citation

  • Léonard, C., 1987. "Large deviations and law of large numbers for a mean field type interacting particle systems," Stochastic Processes and their Applications, Elsevier, vol. 25, pages 215-235.
    • Handle: RePEc:eee:spapps:v:25:y:1987:i::p:215-235
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