About Hydrodynamic Limit of Some Exclusion Processes via Functional Integration

Guy Fayolle 1 Cyril Furtlehner 2
2 TAO - Machine Learning and Optimisation
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LRI - Laboratoire de Recherche en Informatique
Abstract : This article considers some classes of models dealing with the dynamics of discrete curves subjected to stochastic deformations. It turns out that the problems of interest can be set in terms of interacting exclusion processes, the ultimate goal being to derive hydrodynamic limits after proper scalings. A seemingly new method is proposed, which relies on the analysis of specific partial differential operators, involving variational calculus and functional integration: indeed, the variables are the values of some functions at given points, the number of which tends to become infinite, which requires the construction of generalized measures. Starting from a detailed analysis of the ASEP system on the torus Z/NZ, we claim that the arguments a priori work in higher dimensions (ABC, multi-type exclusion processes, etc), leading to sytems of coupled partial differential equations of Burgers' type.
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https://hal.inria.fr/hal-00662674
Contributor : Guy Fayolle <>
Submitted on : Tuesday, January 24, 2012 - 4:52:00 PM
Last modification on : Friday, May 25, 2018 - 12:02:03 PM
Long-term archiving on : Wednesday, April 25, 2012 - 2:51:37 AM

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  • HAL Id : hal-00662674, version 1
  • ARXIV : 1201.5185

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Guy Fayolle, Cyril Furtlehner. About Hydrodynamic Limit of Some Exclusion Processes via Functional Integration. International Mathematical Conference "50 YEARS OF IITP", Institute for Information Transmission Problems (Russian Academy of Sciences), Jul 2011, Moscow, Russia. ⟨hal-00662674⟩

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