| Publication type: |
 |
Preprint, Working Paper, ... |
|
| Subject: |
|
Mathematics/Probability
|
|
| Title: |
|
Type transition of simple random walks on randomly directed regular lattices |
|
| Author(s): |
|
Massimo Campanino 1, Dimitri Petritis ( ,  ) 2 |
|
| Laboratory: |
|
|
|
| Abstract: |
|
Simple random walks on a partially directed version of $\mathbb{Z}^2$ are considered. More precisely, vertical edges between neighbouring vertices of $\mathbb{Z}^2$ 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. |
|
| Fulltext language: |
|
English |
|
| Production date: |
|
2012-04-24 |
|
|
| Keyword(s): |
|
Markov chain – random environment – recurrence criteria – random graphs – directed graphs. |
|
| Classification: |
|
60J10, 60K20 |
|
| Comment: |
|
27 pages |
|
|
Export this paper
