scholarly journals Amenable ergodic group actions and an application to Poisson boundaries of random walks

1978 ◽  
Vol 27 (3) ◽  
pp. 350-372 ◽  
Author(s):  
Robert J Zimmer
Keyword(s):  
Random Walks ◽  
Group Actions

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.

Non-homogeneous Random Walks

2016 ◽  
Author(s):  
Mikhail Menshikov ◽  
Serguei Popov ◽  
Andrew Wade
Keyword(s):  
Random Walks

Recurrence of Symmetric Random Walks.

1983 ◽  
Author(s):  
S. W. Dharmadhikari ◽  
Kumar Joag-dev
Keyword(s):  
Random Walks
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