2020/02/13 by Daniel Camarena, Camarena, Daniel, Gonzalo Panizo +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #60G50 #82C41 #Diffusion and Search Dynamics #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2002.05750
openalex publication_date 2020/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The balanced excited random walk, introduced by Benjamini, Kozma and Schapira in 2011, is defined as a discrete time stochastic process in \mathbb Zd, depending on two integer parameters 1≤ d1,d2≤ d, which whenever it is at a site x∈\mathbb Zd at time n, it jumps to x± ei with uniform probability, where e1,…,ed are the canonical vectors, for 1≤ i≤ d1, if the site x was visited for the first time at time n, while it jumps to x± ei with uniform probability, for 1+d-d2≤ i≤ d, if the site x was already visited before time n. Here we give an overview of this model when d1+d2=d and introduce and study the cases when d1+d2>d. In particular, we prove that for all the cases d≥ 5 and most cases d=4, the balanced excited random walk is transient.