McKean-Vlasov limit for interacting random processes in random media |
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Authors: | Paolo Dai Pra Frank den Hollander |
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Affiliation: | (1) Dipartimento di Matematica Pura e Applicata, Universitá di Padova, 35131 Padova, Italy;(2) Mathematical Institute, University of Nijmegen, 6525 ED Nijmegen, The Netherlands |
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Abstract: | We apply large-deviation theory to particle systems with a random mean-field interaction in the McKean-Vlasov limit. In particular, we describe large deviations and normal fluctuations around the McKean-Vlasov equation. Due to the randomness in the interaction, the McKean-Vlasov equation is a collection of coupled PDEs indexed by the state space of the single components in the medium. As a result, the study of its solution and of the finite-size fluctuation around this solution requires some new ingredient as compared to existing techniques for nonrandom interaction. |
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Keywords: | Interacting particle systems random media McKean-Vlasov equation large deviations central limit theorem |
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