标题： 近视非交集在一个周期势中 显示英文标题

标题： Myopic non-intersection in a periodic potential

摘要： 我们引入了一类马尔可夫过程，这些过程被限制在一个长度为 T > 0 的移动时间窗口内避免相交，我们将这种设置称为近视非相交。特别地，我们研究了一组受到周期势约束的近视非相交布朗运动。我们的重点在于理解势场的约束效应与由非相交约束引起的排斥作用之间的相互作用。我们证明，在长时间极限下，当 T 和势场强度都变得很大时，该模型收敛到一组近视非相交随机游走，其动态在标准非相交动力学和排斥行为之间切换。本文的主要技术贡献是一种算法的提出，该算法基于接受-拒绝抽样方案的修改，提供了近视约束系统的显式构造。 显示英文摘要

摘要： We introduce a class of Markov processes conditioned to avoid intersection over a moving time window of length T>0, a setting we refer to as myopic non-intersection. In particular, we study a system of myopic non-intersecting Brownian motions subject to a periodic potential. Our focus lies in understanding the interplay between the confining effect of the potential and the repulsion induced by the non-intersection constraint. We show that, in the long time limit, and as both T and the strength of the potential become large, the model converges to a system of myopic non-intersecting random walks, which transitions between standard non-intersection dynamics and exclusion behavior. The main technical contribution of the paper is the introduction of an algorithm, based on a modification of the acceptance-rejection sampling scheme, that provides an explicit construction of myopically constrained systems.