基于预解式与$H^1$逼近的超临界两物种零程过程中的凝聚与亚稳态
Condensation and metastability in the supercritical two-species zero-range process via resolvent and $H^1$-approximation
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中文总结 AI 辅助
本文研究超临界两物种零程过程，结合预解式与$H^1$逼近方法，严格刻画单凝聚体位置的动力学亚稳态行为，其运动由加速时间尺度上的马尔可夫链支配。
中文摘要 AI 辅助
本文研究两物种零程过程，即经典零程过程的多物种推广。首先分析其凝聚态，这与单物种对应情况直接平行。主要结果是建立了单凝聚体位置的动力学亚稳态行为，表明其运动由加速时间尺度$N^{1+\boldsymbol{\u03b1}}$上的简单马尔可夫链支配，其中$N$为系统总粒子数，参数$\boldsymbol{\u03balpha}>1$表征系统的吸引性。本工作的另一创新在于证明技术，将新近发展的预解式方法与$H^1$逼近方法相结合，以严格刻画亚稳态。
英文摘要
In this article, we investigate the two-species zero-range process, a multi-species generalization of the classical zero-range process. First, we analyze its condensation regime, which directly parallels its single-species counterpart. As our main result, we establish the dynamical metastable behavior of the location of the single condensate, showing that its motion is governed by a simple Markov chain on the accelerated time scale $N^{1+α}$, where $N$ denotes the total number of particles in the system and the parameter $α>1$ governs the attractivity of the system. Another novelty of this work lies in the proof technique, which integrates the recently developed resolvent approach with the $H^{1}$-approximation method to rigorously characterize metastability.
发表机构
- Yonsei University（延世大学）
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