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Hydrodynamic limit of condensing two-species zero range processes with sub-critical initial profiles | | Nicolas Dirr
; Marios G. Stamatakis
; Johannes Zimmer
; | | Date: |
14 Oct 2016 | | 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 mean zero two-species condensing zero range processes
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. | | Source: | arXiv, 1610.4358 | | Services: | Forum | Review | PDF | Favorites | |
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