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• W2962760420 endingPage "4269" @default.
• W2962760420 startingPage "4239" @default.
• W2962760420 abstract "Let $(X, cal B, nu)$ be a probability space and let $Gamma$be a countable group of $nu$-preserving invertible maps of $X$ intoitself. To a probability measure $mu$ on $Gamma$ corresponds arandom walk on $X$ with Markov operator $P$ given by $Ppsi(x) =sum_{a} psi(ax) , mu(a)$. We consider various examples ofergodic $Gamma$-actions and random walks and their extensions by avector space: groups of automorphisms or affine transformations oncompact nilmanifolds, random walks in random scenery on non amenablegroups, translations on homogeneous spaces of simple Lie groups,random walks on motion groups. A powerful tool in this study is thespectral gap property for the operator $P$ when it holds. We use itto obtain limit theorems, recurrence/transience property andergodicity for random walks on non compact extensions of thecorresponding dynamical systems." @default.
• W2962760420 created "2019-07-30" @default.
• W2962760420 creator A5007172280 @default.
• W2962760420 creator A5040981690 @default.
• W2962760420 date "2013-01-01" @default.
• W2962760420 modified "2023-10-18" @default.
• W2962760420 title "Ergodicity of group actions and spectral gap, applications to random walks and Markov shifts" @default.
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• W2962760420 doi "https://doi.org/10.3934/dcds.2013.33.4239" @default.
• W2962760420 hasPublicationYear "2013" @default.
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