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February 2008 Time regularity for aperiodic or irreducible random walks on groups
Nick DUNGEY
Hokkaido Math. J. 37(1): 19-40 (February 2008). DOI: 10.14492/hokmj/1253539584

Abstract

This paper studies time regularity for the random walk governed by a probability measure $\mu$ on a locally compact, compactly generated group $G$. If $\mu$ is eventually coset aperiodic on $G$ and satisfies certain additional conditions, we establish that the associated Markov operator $T_{\mu}$ is analytic in $L^2(G)$, that is, one has an estimate $\|(I-T_{\mu}) T_{\mu}^n \| \leq cn^{-1}$, $n\in \mathbb{N}$, in $L^2$ operator norm. Alternatively, if $\mu$ is irreducible with period $d$ and satisfies certain conditions, we show that $T_{\mu}^d$ is analytic in $L^2(G)$. To obtain these results, we develop a number of interesting algebraic and spectral properties of coset aperiodic or irreducible measures on groups.

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Nick DUNGEY. "Time regularity for aperiodic or irreducible random walks on groups." Hokkaido Math. J. 37 (1) 19 - 40, February 2008. https://doi.org/10.14492/hokmj/1253539584

Information

Published: February 2008
First available in Project Euclid: 21 September 2009

zbMATH: 1143.60313
MathSciNet: MR2395076
Digital Object Identifier: 10.14492/hokmj/1253539584

Subjects:
Primary: 60G50
Secondary: 22D05, 60B15

Rights: Copyright © 2008 Hokkaido University, Department of Mathematics

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Vol.37 • No. 1 • February 2008
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