TY - JOUR

T1 - Hydrodynamic Limit of Condensing Two-Species Zero Range Processes with Sub-critical Initial Profiles

AU - Dirr, Nicolas

AU - Stamatakis, Marios G.

AU - Zimmer, Johannes

N1 - Publisher Copyright:
© 2017, The Author(s).

PY - 2017/8/1

Y1 - 2017/8/1

N2 - 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.

AB - 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.

KW - Comparison principles for systems of PDEs

KW - Condensing zero range processes

KW - Hydrodynamic limit

KW - Zero range processes

UR - http://www.scopus.com/inward/record.url?scp=85021744408&partnerID=8YFLogxK

U2 - 10.1007/s10955-017-1827-6

DO - 10.1007/s10955-017-1827-6

M3 - Article

AN - SCOPUS:85021744408

SN - 0022-4715

VL - 168

SP - 794

EP - 825

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 4

ER -