TY - JOUR

T1 - Functional central limit theorem for random walks in random environment defined on regular trees

AU - Collevecchio, Andrea

AU - Takei, Masato

AU - Uematsu, Yuma

PY - 2020/8

Y1 - 2020/8

N2 - We study Random Walks in an i.i.d. Random Environment (RWRE) defined on b-regular trees. We prove a functional central limit theorem (FCLT) for transient processes, under a moment condition on the environment. We emphasize that we make no uniform ellipticity assumptions. Our approach relies on regenerative levels, i.e. levels that are visited exactly once. On the way, we prove that the distance between consecutive regenerative levels have a geometrically decaying tail. In the second part of this paper, we apply our results to Linearly Edge-Reinforced Random Walk (LERRW) to prove FCLT when the process is defined on b-regular trees, with b≥4, substantially improving the results of the first author (see Theorem 3 of Collevecchio (2006)).

AB - We study Random Walks in an i.i.d. Random Environment (RWRE) defined on b-regular trees. We prove a functional central limit theorem (FCLT) for transient processes, under a moment condition on the environment. We emphasize that we make no uniform ellipticity assumptions. Our approach relies on regenerative levels, i.e. levels that are visited exactly once. On the way, we prove that the distance between consecutive regenerative levels have a geometrically decaying tail. In the second part of this paper, we apply our results to Linearly Edge-Reinforced Random Walk (LERRW) to prove FCLT when the process is defined on b-regular trees, with b≥4, substantially improving the results of the first author (see Theorem 3 of Collevecchio (2006)).

KW - Functional central limit theorem

KW - Random walks in random environment

KW - Self-interacting random walks

UR - http://www.scopus.com/inward/record.url?scp=85080078701&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2020.02.004

DO - 10.1016/j.spa.2020.02.004

M3 - Article

AN - SCOPUS:85080078701

VL - 130

SP - 4892

EP - 4909

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 8

ER -