1998-12-01
Random walks on almost connected locally compact groups: Boundary and convergence
Publication
Publication
Journal d'Analyse Mathematique , Volume 74 p. 235- 273
We prove that, given an arbitrary spread out probability measure μ on an almost connected locally compact second countable group G, there exists a homogeneous space G/H, called the μ-boundary, such that the space of bounded μ-harmonic functions can be identified with L∞(G/H). The μ-boundary is an amenable contractive homogeneous space. We also establish that the canonical projection onto the μ-boundary of the right random walk of law μ always converges in probability and, when G is amenable, it converges almost surely. The μ-boundary can be characterised as the largest homogeneous space among those homogeneous spaces in which the canonical projection of the random walk converges in probability.
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Journal d'Analyse Mathematique | |
Organisation | School of Mathematics and Statistics |
Jaworski, W. (1998). Random walks on almost connected locally compact groups: Boundary and convergence. Journal d'Analyse Mathematique, 74, 235–273.
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