Electronic Journal of Probability
- Electron. J. Probab.
- Volume 20 (2015), paper no. 62, 14 pp.
The most visited sites of biased random walks on trees
We consider the slow movement of randomly biased random walk $(X_n)$ on a supercritical Galton-Watson tree, and are interested in the sites on the tree that are most visited by the biased random walk. Our main result implies tightness of the distributions of the most visited sites under the annealed measure. This is in contrast with the one-dimensional case, and provides, to the best of our knowledge, the first non-trivial example of null recurrent random walk whose most visited sites are not transient, a question originally raised by Erdős and Révész for simple symmetric random walk on the line.
Electron. J. Probab., Volume 20 (2015), paper no. 62, 14 pp.
Accepted: 10 June 2015
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
This work is licensed under aCreative Commons Attribution 3.0 License.
Hu, Yueyun; Shi, Zhan. The most visited sites of biased random walks on trees. Electron. J. Probab. 20 (2015), paper no. 62, 14 pp. doi:10.1214/EJP.v20-4051. https://projecteuclid.org/euclid.ejp/1465067168