Brownian motion, harmonic functions and hyperbolicity for Euclidean complexes

Michael Brin*, Yuri Kifer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

A Euclidean complex X is a simplicial complex whose simplices are (flat) Euclidean simplices. We construct a natural Brownian motion on X and show that if X has nonpositive curvature and satisfies Gromov's hyperbolicity condition, then, with probability one, Brownian motion tends to a random limit on the Gromov boundary. Applying a combination of geometric and probabilistic techniques we describe spaces of harmonic functions on X.

Original languageEnglish
Pages (from-to)421-468
Number of pages48
JournalMathematische Zeitschrift
Volume237
Issue number3
DOIs
StatePublished - Jul 2001

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