An overview of the balanced excited random walk [article]

Daniel Camarena, Gonzalo Panizo, Alejandro F. Ramírez
2020 arXiv   pre-print
The balanced excited random walk, introduced by Benjamini, Kozma and Schapira in 2011, is defined as a discrete time stochastic process in Z^d, depending on two integer parameters 1< d_1,d_2< d, which whenever it is at a site x∈Z^d at time n, it jumps to x± e_i with uniform probability, where e_1,...,e_d are the canonical vectors, for 1< i< d_1, if the site x was visited for the first time at time n, while it jumps to x± e_i with uniform probability, for 1+d-d_2< i< d, if the site x was already
more » ... visited before time n. Here we give an overview of this model when d_1+d_2=d and introduce and study the cases when d_1+d_2>d. In particular, we prove that for all the cases d> 5 and most cases d=4, the balanced excited random walk is transient.
arXiv:2002.05750v2 fatcat:wpqnqydw65benkztvcsepqqvy4