Biased Random Walks and Exclusion Processes on Random Graphs

&gt；我们考虑d维空间中梯形图或格的随机生成树以及点过程。它们充当有偏见的随机行走或排除过程的随机环境。我们计划研究(1)随机行走的速度作为偏差的函数；(2)标记粒子在排除过程中的速度；(3)分别对步行者或标记粒子的位置的限制规律。对于整数格的生成树，我们计划考虑“向外有偏”的随机游动，并研究同样的问题。我们计划研究点过程上的有偏随机游动，将Faggionato，Gantert和Sali在早期工作中的一维结果推广到多维情形。

>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.