Communications in Mathematical Sciences
Volume 17 (2019)
A variational structure for interacting particle systems and their hydrodynamic scaling limits
Pages: 739 – 780
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.
interacting particle systems, macroscopic fluctuation theory, large deviations, action functionals, $\Gamma$-convergence
2010 Mathematics Subject Classification
35Q35, 76M28, 82C22
Copyright © 2019 M. Kaiser, R. L. Jack and J. Zimmer
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.
Received 10 July 2018
Accepted 22 January 2019
Published 30 August 2019