Large Deviations for Diffusions Interacting Through Their Ranks
| Autor: | Srinivasa R. S. Varadhan, Ofer Zeitouni, Mykhaylo Shkolnikov, Amir Dembo |
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| Rok vydání: | 2016 |
| Předmět: |
Convection
Applied Mathematics General Mathematics Cumulative distribution function media_common.quotation_subject 010102 general mathematics Infinity 01 natural sciences 010104 statistics & probability Large deviations theory Statistical physics 0101 mathematics Diffusion (business) Particle density Porous medium Rate function media_common Mathematics |
| Zdroj: | Communications on Pure and Applied Mathematics. 69:1259-1313 |
| ISSN: | 0010-3640 |
| DOI: | 10.1002/cpa.21640 |
| Popis: | We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of the approriate McKean-Vlasov equation and that the corresponding cumulative distribution function evolves according to the porous medium equation with convection. The large deviations rate function is provided in explicit form. This is the first instance of a LDP for interacting diffusions, where the interaction occurs both through the drift and the diffusion coefficients and where the rate function can be given explicitly. In the course of the proof, we obtain new regularity results for a certain tilted version of the porous medium equation. |
| Databáze: | OpenAIRE |
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