Hydrodynamic limit of condensing two-species zero range processes with sub-critical initial profiles

Johannes Zimmer, Nicolas Dirr, Marios Stamatakis

Research output: Contribution to journalArticle

Abstract

Two-species condensing zero range processes (ZRPs) are interacting particle systems with two species of particles and zero range interaction exhibiting phase separation outside a domain of sub-critical densities. We prove the hydrodynamic limit of nearest neighbour mean zero two-species condensing ZRP with bounded local jump rate for sub-critical initial profiles, i.e., for initial profiles whose image is contained in the region of sub-critical densities. The proof is based on H.T. Yau’s relative entropy method, which relies on the existence of sufficiently regular solutions to the hydrodynamic equation. In the particular case of the species-blind ZRP, we prove that the solutions of the hydrodynamic equation exist globally in time and thus the hydrodynamic limit is valid for all times.

Original languageEnglish
Pages (from-to)794–825
JournalJournal of Statistical Physics
Volume168
Issue number4
Early online date1 Jul 2017
DOIs
Publication statusPublished - Aug 2017

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Zero-range Process
Hydrodynamic Limit
condensing
hydrodynamic equations
hydrodynamics
Hydrodynamic Equations
profiles
entropy
Entropy Method
Interacting Particle Systems
Regular Solution
Relative Entropy
Phase Separation
Zero
Nearest Neighbor
Jump
interactions
Valid
Profile
Interaction

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Hydrodynamic limit of condensing two-species zero range processes with sub-critical initial profiles. / Zimmer, Johannes; Dirr, Nicolas; Stamatakis, Marios.

In: Journal of Statistical Physics, Vol. 168, No. 4, 08.2017, p. 794–825.

Research output: Contribution to journalArticle

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