Results 1  10
of
10
Property (T) and the Furstenberg Entropy of Nonsingular Actions
, 2014
"... We establish a new characterization of property (T) in terms of the Furstenberg entropy of nonsingular actions. Given any generating measure µ on a countable group G, A. Nevo showed that a necessary condition for G to have property (T) is that the Furstenberg µentropy values of the ergodic, properl ..."
Abstract
 Add to MetaCart
We establish a new characterization of property (T) in terms of the Furstenberg entropy of nonsingular actions. Given any generating measure µ on a countable group G, A. Nevo showed that a necessary condition for G to have property (T) is that the Furstenberg µentropy values of the ergodic
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 ..."
Abstract

Cited by 7 (6 self)
 Add to MetaCart
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
FURSTENBERG ENTROPY REALIZATIONS FOR VIRTUALLY FREE GROUPS AND LAMPLIGHTER GROUPS
, 1210
"... 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 ..."
Abstract
 Add to MetaCart
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
An abramov formula for stationary spaces of discrete groups, arXiv preprint arXiv:1204.5414
, 2012
"... Abstract. Let (G, µ) be a discrete group equipped with a generating probability measure, and let Γ be a finite index subgroup of G. A µrandom walk on G, starting from the identity, returns to Γ with probability one. Let θ be the hitting measure, or the distribution of the position in which the rand ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
the random walk first hits Γ. We prove that the Furstenberg entropy of a (G, µ)stationary space, with respect to the action of (Γ, θ), is equal to the Furstenberg entropy with respect to the action of (G, µ), times the index of Γ in G. The index is shown to be equal to the expected return time to Γ. As a
ENTROPY THEORY WITHOUT PAST
, 1998
"... This paper treats the Pinsker algebra of a dynamical system in a way which avoids the use of an ordering on the acting group. This enables us to prove some of the classical results about entropy and the Pinsker algebra in the general setup of measure preserving dynamical systems, where the acting g ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
group is a discrete countable amenable group. We prove a basic disjointness theorem which asserts the relative disjointness in the sense of Furstenberg, of 0entropy extensions from completely positive entropy (c.p.e.) extensions. This theorem is used to prove several classical results in the general
Entropy Theory without Past
, 1998
"... . This paper treats the Pinsker algebra of a dynamical system in a way which avoids the use of an ordering on the acting group. This enables us to prove some of the classical results about entropy and the Pinsker algebra in the general setup of measure preserving dynamical systems, where the acting ..."
Abstract
 Add to MetaCart
group is a discrete countable amenable group. We prove a basic disjointness theorem which asserts the relative disjointness in the sense of Furstenberg, of 0entropy extensions from completely positive entropy (c.p.e.) extensions. This theorem is used to prove several classical results in the general
Local entropy averages and projections of fractal measures
, 2009
"... Abstract. We show that for families of measures on Euclidean space which satisfy an ergodictheoretic form of “selfsimilarity ” under the operation of rescaling, the dimension of linear images of the measure behaves in a semicontinuous way. We apply this to prove the following conjecture of Furst ..."
Abstract

Cited by 26 (11 self)
 Add to MetaCart
of Furstenberg: if X,Y ⊆ [0, 1] are closed and invariant, respectively, under ×m mod 1 and ×n mod 1, where m,n are not powers of the same integer, then, for any t 6 = 0, dim(X + tY) = min{1, dimX + dimY}. A similar result holds for invariant measures, and gives a simple proof of the RudolphJohnson theorem. Our
AN INFINITE MEASURE INVARIANT FOR ×2, ×3
"... Abstract. Furstenberg conjectured that any continuous probability measure ν on [0, 1) invariant under multiplication by two and multiplication by three (denoted by R2(x) = 2x mod 1 and R3(x) = 3x mod 1) must be Lebesgue measure. Lyons showed this under the additional assumption that ν is exact for ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
for at least one of the transformations. Rudolph established Furstenberg’s conjecture under the weaker assumptions that ν is ergodic under R2 and R3 jointly and has positive entropy for at least one of the transformations. The general conjecture however, remains open. In this note, we go in a different