Biased Random Walks and Exclusion Processes on Random Graphs

我们考虑阶梯图或格的随机生成树，以及d维空间中的点过程。它们作为有偏见的随机漫步或排除过程的随机环境。我们计划研究(1)随机漫步的速度作为偏差的函数；(2)被标记粒子在排除过程中的速度；(3)步行者或被标记粒子的位置限制规律。对于整数格的生成树，我们计划考虑“向外偏置”随机漫步并研究相同的问题。我们计划研究点过程上的有偏随机漫步，将Faggionato， Gantert和Salvi早期工作中的一维结果推广到多维情况。

>We consider random spanning trees of ladder graphs or lattices, as well as point processes in d-dimensional space. They serve as random environments for biased random walks or exclusion processes. We plan to investigate (1) the speed of the random walk as a function of the bias; (2) the speed of the tagged particle in the exclusion process; (3) limit laws for the position of the walker or tagged particle, respectively. For spanning trees of integer lattices, we plan to consider "outwards biased'' random walks and study the same questions. We plan to investigate biased random walks on point processes, generalizing the one-dimensional results in earlier work by Faggionato, Gantert and Salvi to the multidimensional case.