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A variational structure for interacting particle systems and their hydrodynamic scaling limits

Published version
Peer-reviewed

Type

Article

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Authors

Kaiser, Marcus 
Jack, Robert L 
Zimmer, Johannes 

Abstract

We consider hydrodynamic scaling limits for a class of reversible interacting particle systems, which includes the symmetric simple exclusion process and certain zero-range processes. We study a (non-quadratic) microscopic action functional for these systems. We analyse the behaviour of this functional in the hydrodynamic limit and we establish conditions under which it converges to the (quadratic) action functional of Macroscopic Fluctuation Theory. We discuss the implications of these results for rigorous analysis of hydrodynamic limits.

Description

Keywords

Interacting Particle Systems, Macroscopic Fluctuation Theory, Large Deviations, action functionals, Gamma-convergence

Journal Title

Communications in Mathematical Sciences

Conference Name

Journal ISSN

1539-6746
1945-0796

Volume Title

17

Publisher

International Press of Boston, Inc.
Sponsorship
M.K. is supported by a scholarship from the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa), under the project EP/L015684/1. J.Z. gratefully acknowledges funding by the EPSRC through project EP/K027743/1, the Leverhulme Trust (RPG-2013-261) and a Royal Society Wolfson Research Merit Award.