Electronic Journal of Probability
- Electron. J. Probab.
- Volume 15 (2010), paper no. 36, 1143-1160.
Entropy of Random Walk Range on Uniformly Transient and on Uniformly Recurrent Graphs
We study the entropy of the distribution of the set $R_n$ of vertices visited by a simple random walk on a graph with bounded degrees in its first n steps. It is shown that this quantity grows linearly in the expected size of $R_n$ if the graph is uniformly transient, and sublinearly in the expected size if the graph is uniformly recurrent with subexponential volume growth. This in particular answers a question asked by Benjamini, Kozma, Yadin and Yehudayoff (preprint).
Electron. J. Probab., Volume 15 (2010), paper no. 36, 1143-1160.
Accepted: 7 July 2010
First available in Project Euclid: 1 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60J05: Discrete-time Markov processes on general state spaces
This work is licensed under aCreative Commons Attribution 3.0 License.
Windisch, David. Entropy of Random Walk Range on Uniformly Transient and on Uniformly Recurrent Graphs. Electron. J. Probab. 15 (2010), paper no. 36, 1143--1160. doi:10.1214/EJP.v15-787. https://projecteuclid.org/euclid.ejp/1464819821