Quenched convergence and strong local equilibrium for asymmetric zero-range process with site disorder

• 成果类型: Article
• 署名作者: Bahadoran, C.; Mountford, T.; Ravishankar, K.; Saada, E.
• 署名单位: Universite Clermont Auvergne (UCA); Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; New York University; NYU Shanghai; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-019-00916-2
• 发表日期: 2020
• 页码: 149-202
• 关键词: attractive particle-systems; hydrodynamics; BEHAVIOR; limit

摘要

We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded nondecreasing function of the number of particles. We prove quenched strong local equilibrium at subcritical and critical hydrodynamic densities, and dynamic local loss of mass at supercritical hydrodynamic densities. Our results do not assume starting from local Gibbs states. As byproducts of these results, we prove convergence of the process from given initial configurations with an asymptotic density of particles to the left of the origin. In particular, we relax the weak convexity assumption of Bahadoran et al. (Braz J Probab Stat 29(2):313-335, 2015; Ann Inst Henri Poincare Probab Stat 53(2):766-801, 2017) for the escape of mass property.