发表机构
Durham University; University of Porto（杜伦大学; 波尔图大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究随机环境下排斥粒子系统的云分解，揭示Sinai机制下深势阱导致粒子堵塞，形成速度指数递减的稳定云，并给出分布极限。
AI 中文摘要
我们考虑整数格上具有排斥相互作用的连续时间粒子系统。每个粒子通过从共同随机环境中独立抽取的方式被赋予固有的左、右跳跃率。我们确定了系统分解为最大稳定子系统（我们称之为云）的分解方式。我们展示了对应于随机环境律的不同机制下，云分解的不同定性行为，这些机制与一维随机环境随机游走中的经典Sinai和Kesten--Kozlov--Spitzer机制相平行。我们在Sinai机制下的主要结果是，系统被分解为无穷多个有限云，这些云都以快速递减的速度大小趋向负无穷，并且我们获得了相关的显式分布极限。我们通过随机环境相关的势函数来分析该模型。在Sinai机制下，深势阱捕获粒子，产生稳定的云，其速度在阱深上呈指数级小。由于连续的阱更深，产生的云依次更慢。因此，Sinai随机游走的局域化机制在此表现为一种堵塞现象，其中势阱捕获的不是一个游走者，而是一整块相互排斥的粒子。
英文摘要
We consider a continuous-time particle system with exclusion interaction on the integer lattice. Each particle is assigned intrinsic left and right jump rates by an independent draw from a common random environment. We identify the decomposition of the system into maximal stable subsystems, which we call clouds. We show different qualitative behaviour for the cloud decomposition corresponding to different regimes for the random environment law that parallel the classical Sinai and Kesten--Kozlov--Spitzer regimes from one-dimensional random walk in random environment. Our main result in the Sinai regime is that the system is decomposed into an infinite number of finite clouds which all go to minus infinity with rapidly decreasing speed magnitudes, and we obtain explicit associated distributional limits. We analyse the model through the potential function associated with the random environment. In the Sinai regime, deep potential wells trap particles, producing stable clouds whose speeds are exponentially small in the well depth. Since successive wells are deeper, the resulting clouds are successively slower. Thus the localization mechanism of Sinai's random walk manifests itself here as a jamming phenomenon, in which a potential well traps not one walker but an entire block of mutually excluding particles.
Comments39 pages, 11 figures
