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 language | English |
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Pages (from-to) | 421-468 |
Number of pages | 48 |
Journal | Mathematische Zeitschrift |
Volume | 237 |
Issue number | 3 |
DOIs | |
State | Published - Jul 2001 |