Open Access
Translator Disclaimer
September 2013 Harmonic maps on amenable groups and a diffusive lower bound for random walks
James R. Lee, Yuval Peres
Ann. Probab. 41(5): 3392-3419 (September 2013). DOI: 10.1214/12-AOP779

Abstract

We prove diffusive lower bounds on the rate of escape of the random walk on infinite transitive graphs. Similar estimates hold for finite graphs, up to the relaxation time of the walk. Our approach uses nonconstant equivariant harmonic mappings taking values in a Hilbert space. For the special case of discrete, amenable groups, we present a more explicit proof of the Mok–Korevaar–Schoen theorem on the existence of such harmonic maps by constructing them from the heat flow on a Følner set.

Citation

Download Citation

James R. Lee. Yuval Peres. "Harmonic maps on amenable groups and a diffusive lower bound for random walks." Ann. Probab. 41 (5) 3392 - 3419, September 2013. https://doi.org/10.1214/12-AOP779

Information

Published: September 2013
First available in Project Euclid: 12 September 2013

zbMATH: 1284.05250
MathSciNet: MR3127886
Digital Object Identifier: 10.1214/12-AOP779

Subjects:
Primary: 20F65 , 60B15 , 60G42 , 60J45

Keywords: Harmonic Maps , random walks on groups , Rate of escape

Rights: Copyright © 2013 Institute of Mathematical Statistics

JOURNAL ARTICLE
28 PAGES


SHARE
Vol.41 • No. 5 • September 2013
Back to Top