Previous issue ·  Next issue ·  Recently posted articles ·  Most recent issue · All issues   
Home Overview Authors Editorial Contact Subscribe

Moscow Mathematical Journal

Volume 19, Issue 1, January–March 2019  pp. 51–76.

Regular and Singular Continuous Time Random Walk in Dynamic Random Environment

Authors:  C. Boldrighini (1), A. Pellegrinotti (2), and E. A. Zhizhina (3)
Author institution:(1) Istituto Nazionale di Alta Matematica (INdAM), GNFM, Unità locale Università Roma Tre, Largo S. Leonardo Murialdo, 1, 00146 Rome, Italy
(2) Dipartimento di Matematica e Fisica, Università di Roma Tre, Largo S. Leonardo Murialdo 1, 00146 Rome, Italy
(3) Institute for Information Transmission Problems, Russian Academy of Sciences


We consider a homogeneous continuous-time random walk (CTRW) on the lattice ℤd, d = 1, 2, ..., which is a kind of random trap model in a time-dependent (“dynamic”) environment. The waiting time distribution is renewed at each jump, and is given by a general probability density depending on a parameter η>0 such that the average waiting time is finite for η>1 and infinite for η∈(0, 1]. By applying analytic methods introduced in a previous paper we prove that the asymptotics of the quenched CTRW and of its annealed version are the same for all η>0 and d>1. We also exhibit explicit formulas for the correction term to the quenched asymptotics. For the border-line case η=1 we find an explicit expression for the annealed limiting distribution, which is, to our knowledge, new.

2010 Math. Subj. Class. 60J10, 60K37, 82B41.

Keywords: Continuous-time random walk, random traps, dynamic random environment, singular waiting time, random walk in quenched environment.

Contents   Full-Text PDF