Random walk in a stratified independent random environment

Julien Brémont (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We study Markov chains on a lattice in a codimension-one stratified independent random environment, exploiting results established in [2]. First of all the random walk is transient in dimension at least three. Focusing on dimension two, both recurrence and transience can happen, but transience remains by far the most general situation. We identify the critical scale of the local drift along the strata corresponding to the frontier between the two regimes.

Version 2, corrected and extended.

Domaines: Probabilités [math.PR]; Systèmes dynamiques [math.DS]

Julien Brémont. Random walk in a stratified independent random environment. Electronic Communications in Probability, 2019, 24 (47), pp.1-15. ⟨hal-01922157v2⟩