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FURSTENBERG ENTROPY REALIZATIONS FOR VIRTUALLY FREE GROUPS AND LAMPLIGHTER GROUPS
"... Abstract. Let (G, µ) be a discrete group with a generating probability measure. Nevo shows that if G has property (T) then there exists an ε> 0 such that the Furstenberg entropy of any (G, µ)stationary space is either zero or larger than ε. Virtually free groups, such as SL2(Z), do not have prop ..."
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Abstract. Let (G, µ) be a discrete group with a generating probability measure. Nevo shows that if G has property (T) then there exists an ε> 0 such that the Furstenberg entropy of any (G, µ)stationary space is either zero or larger than ε. Virtually free groups, such as SL2(Z), do not have property (T). For these groups, we construct stationary actions with arbitrarily small, positive entropy. This construction involves building and lifting spaces of lamplighter groups. For some classical lamplighters, these spaces realize a dense set of entropies
Poisson–Furstenberg boundaries of fundamental groups of closed 3manifolds (2014), available at arXiv:1403.2135
"... We obtain a description of Poisson–Furstenberg boundaries for (random walks on) fundamental groups of compact graphmanifolds. Together with previously known results due to V.A. Kaimanovich and others, this allows one to obtain descriptions of Poisson–Furstenberg boundaries for fundamental groups o ..."
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We obtain a description of Poisson–Furstenberg boundaries for (random walks on) fundamental groups of compact graphmanifolds. Together with previously known results due to V.A. Kaimanovich and others, this allows one to obtain descriptions of Poisson–Furstenberg boundaries for fundamental groups of all closed 3manifolds. 1
FURSTENBERG ENTROPY REALIZATIONS FOR VIRTUALLY FREE GROUPS AND LAMPLIGHTER GROUPS
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"... Abstract. Let (G,µ) be a discrete group with a generating probability measure. Nevo shows that if G has property (T) then there exists an ε> 0 such that the Furstenberg entropy of any (G,µ)stationary space is either zero or larger than ε. Virtually free groups, such as SL2(Z), do not have proper ..."
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Abstract. Let (G,µ) be a discrete group with a generating probability measure. Nevo shows that if G has property (T) then there exists an ε> 0 such that the Furstenberg entropy of any (G,µ)stationary space is either zero or larger than ε. Virtually free groups, such as SL2(Z), do not have property (T). For these groups, we construct stationary actions with arbitrarilysmall, positive entropy. This construction involves building and lifting spaces of lamplighter groups. For some classical lamplighters, these spaces realize a dense set of entropies
FURSTENBERG ENTROPY REALIZATIONS FOR VIRTUALLY FREE GROUPS AND LAMPLIGHTER GROUPS
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