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2016 | OriginalPaper | Chapter

The Gradient Flow Approach to Hydrodynamic Limits for the Simple Exclusion Process

Authors : Max Fathi, Marielle Simon

Published in: From Particle Systems to Partial Differential Equations III

Publisher: Springer International Publishing

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Abstract

We present a new approach to prove the macroscopic hydrodynamic behaviour for interacting particle systems, and as an example we treat the well-known case of the symmetric simple exclusion process (SSEP). More precisely, we characterize any possible limit of its empirical density measures as solutions to the heat equation by passing to the limit in the gradient flow structure of the particle system.

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previous chapter The Boltzmann Equation over : Dispersion Versus Dissipation
next chapter Symmetries and Martingales in a Stochastic Model for the Navier-Stokes Equation
Footnotes
1
This is also the assumption used to make Yau’s relative entropy method work, see [21].
 
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Metadata
Title
The Gradient Flow Approach to Hydrodynamic Limits for the Simple Exclusion Process
Authors
Max Fathi
Marielle Simon
Copyright Year
2016
Book
From Particle Systems to Partial Differential Equations III

Print ISBN: 978-3-319-32142-4

Electronic ISBN: 978-3-319-32144-8

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-32144-8_8

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