- Simple random walks on some partially directed planar graphs
- Bosi, Gianluca <1991>
Subject
- MAT/06 Probabilità e Statistica matematica
Description
- In this thesis we analyze the recurrence behavior of simple random walks on some classes of directed planar graphs. Our first model is a version of the honeycomb lattice, where the horizontal edges are randomly oriented according to families of random variables: depending on their distribution, we prove a.s. transience in some cases, and a.s. recurrence in other ones. Our results extend those obtained by Campanino and Petritis (’03 and ’14) for partially oriented square grid lattices. Furthermore, we consider two directed square grid lattices on which, because of the direction imposed by the oriented edges, the simple random walk is bound to revolve clockwise: we prove recurrence for one of the graphs, solving a conjecture of Menshikov et al. (’17), and we give a new proof of transience for the other one.
Date
- 2019-03-22
Type
- Doctoral Thesis
- PeerReviewed
Format
- application/pdf
Identifier
urn:nbn:it:unibo-25225
Bosi, Gianluca (2019) Simple random walks on some partially directed planar graphs, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Matematica