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Entropy of Random Walk Range on Uniformly Transient and on Uniformly Recurrent Graphs

   
@article{EJP787,
	author = {David Windisch},
	title = {Entropy of Random Walk Range on Uniformly Transient and on Uniformly Recurrent Graphs},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {15},
	year = {2010},
	keywords = {random walk, range, entropy},
	abstract = {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).},
	pages = {no. 36, 1143-1160},
	issn = {1083-6489},
	doi = {10.1214/EJP.v15-787},    
        url = {http://ejp.ejpecp.org/article/view/787}}