scholarly journals Ergodicity of group actions and spectral gap, applications to random walks and Markov shifts

2013 ◽  
Vol 33 (9) ◽  
pp. 4239-4269 ◽  
Author(s):  
Jean-Pierre Conze ◽  
◽  
Y. Guivarc'h ◽  
Keyword(s):  
Random Walks ◽  
Spectral Gap ◽  
Group Actions ◽  
Markov Shifts

scholarly journals A Spectral Gap Property for Random Walks Under Unitary Representations

2006 ◽  
Vol 118 (1) ◽  
pp. 141-155 ◽  
Author(s):  
Bachir Bekka ◽  
Yves Guivarc’h
Keyword(s):  
Random Walks ◽  
Spectral Gap ◽  
Unitary Representations

scholarly journals Stable laws and spectral gap properties for affine random walks

2015 ◽  
Vol 51 (1) ◽  
pp. 319-348
Author(s):  
Zhiqiang Gao ◽  
Yves Guivarc’h ◽  
Émile Le Page
Keyword(s):  
Random Walks ◽  
Spectral Gap ◽  
Stable Laws

scholarly journals High Order Random Walks: Beyond Spectral Gap

COMBINATORICA ◽  
2020 ◽  
Vol 40 (2) ◽  
pp. 245-281
Author(s):  
Tali Kaufman ◽  
Izhar Oppenheim
Keyword(s):  
Random Walks ◽  
Spectral Gap ◽  
High Order

scholarly journals Cohomology groups, continuous full groups and continuous orbit equivalence of topological Markov shifts

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Kengo Matsumoto
Keyword(s):  
Group Actions ◽  
Full Group ◽  
Orbit Equivalence ◽  
Cohomology Groups ◽  
Shift Spaces ◽  
Markov Shifts

<p style='text-indent:20px;'>We will study several subgroups of continuous full groups of one-sided topological Markov shifts from the view points of cohomology groups of full group actions on the shift spaces. We also study continuous orbit equivalence and strongly continuous orbit equivalence in terms of these subgroups of the continuous full groups and the cohomology groups.</p>

scholarly journals Extensive amenability and an application to interval exchanges

2016 ◽  
Vol 38 (1) ◽  
pp. 195-219 ◽  
Author(s):  
KATE JUSCHENKO ◽  
NICOLÁS MATTE BON ◽  
NICOLAS MONOD ◽  
MIKAEL DE LA SALLE
Keyword(s):  
Random Walks ◽  
Group Actions ◽  
Interval Exchange ◽  
General Construction ◽  
Poisson Boundary ◽  
Semidirect Products ◽  
Interval Exchange Transformations ◽  
Interval Exchanges ◽  
Probabilistic Proof ◽  
Rational Rank

Extensive amenability is a property of group actions which has recently been used as a tool to prove amenability of groups. We study this property and prove that it is preserved under a very general construction of semidirect products. As an application, we establish the amenability of all subgroups of the group$\text{IET}$of interval exchange transformations that have angular components of rational rank less than or equal to two. In addition, we obtain a reformulation of extensive amenability in terms of inverted orbits and use it to present a purely probabilistic proof that recurrent actions are extensively amenable. Finally, we study the triviality of the Poisson boundary for random walks on$\text{IET}$and show that there are subgroups$G<\text{IET}$admitting no finitely supported measure with trivial boundary.

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