A variational structure for interacting particle systems and their hydrodynamic scaling limits
Published version
Peer-reviewed
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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
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Journal ISSN
1539-6746
1945-0796
1945-0796
Volume Title
17
Publisher
International Press of Boston, Inc.
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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.