2012/04/24 by Massimo Campanino, Campanino, Massimo, Dimitri Petritis +1
Mathematics · Physics and Astronomy · #60J10 #60K20 #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR #msc:60J10 #msc:60K20
paper · pdf · doi:10.48550/arxiv.1204.5297
Accepted for publication in Journal of Applied Probability (2014)
openalex publication_date 2012/04/24 · arxiv created 2014/01/30 · arxiv updated 2014/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Simple random walks on a partially directed version of ℤ2 are considered. More precisely, vertical edges between neighbouring vertices of ℤ2 can be traversed in both directions (they are undirected) while horizontal edges are one-way. The horizontal orientation is prescribed by a random perturbation of a periodic function, the perturbation probability decays according to a power law in the absolute value of the ordinate. We study the type of the simple random walk, i.e. its being recurrent or transient, and show that there exists a critical value of the decay power, above which the walk is almost surely recurrent and below which is almost surely transient.