TY - JOUR
T1 - FURSTENBERG ENTROPY REALIZATIONS FOR VIRTUALLY FREE GROUPS AND LAMPLIGHTER GROUPS
AU - Hartman, Yair
AU - Tamuz, Omer
N1 - Publisher Copyright: © 2015, Hebrew University Magnes Press.
PY - 2015/4/20
Y1 - 2015/4/20
N2 - Let (G, mu) be a discrete group with a generating probability measure. Nevo showed that if G has Kazhdan's property (T), then there exists epsilon > 0 such that the Furstenberg entropy of any (G, mu)-stationary ergodic space is either 0 or larger than epsilon. Virtually free groups, such as SL2(Z), do not have property (T), and neither do their extensions, such as surface groups. For virtually free groups, we construct stationary actions with arbitrarily small, positive entropy. The construction involves building and lifting spaces of lamplighter groups. For some classical lamplighter gropus, these spaces realize a dense set of entropies between 0 and the Poisson boundary entropy.
AB - Let (G, mu) be a discrete group with a generating probability measure. Nevo showed that if G has Kazhdan's property (T), then there exists epsilon > 0 such that the Furstenberg entropy of any (G, mu)-stationary ergodic space is either 0 or larger than epsilon. Virtually free groups, such as SL2(Z), do not have property (T), and neither do their extensions, such as surface groups. For virtually free groups, we construct stationary actions with arbitrarily small, positive entropy. The construction involves building and lifting spaces of lamplighter groups. For some classical lamplighter gropus, these spaces realize a dense set of entropies between 0 and the Poisson boundary entropy.
UR - http://www.scopus.com/inward/record.url?scp=84935006397&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/s11854-015-0016-2
DO - https://doi.org/10.1007/s11854-015-0016-2
M3 - مقالة
SN - 0021-7670
VL - 126
SP - 227
EP - 257
JO - Journal D Analyse Mathematique
JF - Journal D Analyse Mathematique
IS - 1
ER -