We study asymmetric zero-range processes on $$\mathbb {Z}$$ 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 Poincaré Probab Stat 53(2):766–801, 2017 ) for the escape of mass property.

中文翻译：

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具有位点无序的非对称零程过程的淬灭收敛和强局部平衡

我们研究了 $$\mathbb {Z}$$ Z 上的非对称零距离过程，具有最近邻跳跃和站点无序。粒子的跳跃率是粒子数的任意但有界的非递减函数。我们证明了在亚临界和临界流体动力密度下淬灭的强局部平衡，以及在超临界流体动力密度下的动态局部质量损失。我们的结果不假设从本地 Gibbs 状态开始。作为这些结果的副产品，我们证明了从给定初始配置的过程收敛，粒子的渐近密度到原点的左侧。特别是，我们放宽了 Bahadoran 等人的弱凸性假设。（Braz J Probab Stat 29(2):313–335, 2015 ; Ann Inst Henri Poincaré Probab Stat 53(2):766–801, 2017 ）用于逃离大众财产。