Strongly approximately transitive group actions, the Choquet-Deny theorem, and polynomial growth

Jaworski, Wojciech

doi:10.2140/pjm.1994.165.115

Cited by 31 publications

(43 citation statements)

References 8 publications

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“…Strongly approximately transitive group actions were first introduced and studied by W. Jaworski, [19].…”

Section: Sat Dynamical Systemsmentioning

confidence: 99%

“…For more details and basic results concerning general m-stationary dynamical systems and, in particular, m-proximal systems we refer to [13] and [14]. We remind the reader that every m-proximal stationary system is SAT, [19,Corollary 2.4] (see also [14,Proposition 3.7]). For an alternative approach to the Poisson boundary see the seminal work of Kaimanovitch and Vershik [23].…”

Section: M-stationary Dynamical Systemsmentioning

confidence: 99%

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Weak mixing properties for non-singular actions

Glasner¹,

Weiss²

2015

Ergod. Th. Dynam. Sys.

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“…Strongly approximately transitive group actions were first introduced and studied by W. Jaworski, [19].…”

Section: Sat Dynamical Systemsmentioning

confidence: 99%

Section: M-stationary Dynamical Systemsmentioning

confidence: 99%

Weak mixing properties for non-singular actions

Glasner¹,

Weiss²

2015

Ergod. Th. Dynam. Sys.

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“…The aim of this paper is to extend to continuous groups our recent results on strongly approximately transitive actions [9], Let G be a group and X a Borel G-space with a σ-finite quasiinvariant measure a. We denote by L ι {X, a) the space of complex measures absolutely continuous with respect to a and by L\(X,a) C L ι {X,a) the subspace of probability measures.…”

Section: Introductionmentioning

confidence: 99%

Strong approximate transitivity, polynomial growth, and spread out random walks on locally compact groups

Jaworski¹

1995

Pacific J. Math.

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“…G-space. This notion was first introduced by Jaworski in [14]. Finally, we say that (Z, m) is SAT* if it is SAT and if for every g ∈ G, the Radon-Nikodym derivative…”

Section: Non-extremality Of Spherical Meansmentioning

confidence: 99%

Product set phenomena for measured groups

Björklund¹

2017

Ergod. Th. Dynam. Sys.

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Following the works of Furstenberg and Glasner on stationary means, we strengthen and extend in this paper some recent results by Di Nasso, Goldbring, Jin, Leth, Lupini and Mahlburg on piecewise syndeticity of product sets in countable amenable groups to general countable measured groups. We point out several fundamental differences between the behavior of products of "large" sets in Liouville and non-Liouville measured groups.As a (very) special case of our main results, we show that if G is a free group of finite rank, and A and B are "spherically large" subsets of G, then there exists a finite set F ⊂ G such that AFB is thick. The position of the set F is curious, but seems to be necessary; in fact, we can produce left thick sets A, B ⊂ G such that B is "spherically large", but AB is not piecewise syndetic. On the other hand, if A is spherically large, then AA −1 is always piecewise syndetic and left piecewise syndetic. However, contrary to what happens for amenable groups, AA −1 may fail to be syndetic. The same phenomena occur for many other (even amenable, but non-Liouville) measured groups. Our proofs are based on some ergodic-theoretical results concerning stationary actions which should be of independent interest.

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Strongly approximately transitive group actions, the Choquet-Deny theorem, and polynomial growth

Cited by 31 publications

References 8 publications

Weak mixing properties for non-singular actions

Weak mixing properties for non-singular actions

Strong approximate transitivity, polynomial growth, and spread out random walks on locally compact groups

Product set phenomena for measured groups

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