Dimensional Properties of the Harmonic Measure for a Random Walk on a Hyperbolic Group

This paper deals with random walks on isometry groups of Gromov hyperbolic spaces, and more precisely with the dimension of the harmonic measure ν associated with such a random walk. We first establish a link of the form dim ν ≤ h/l between the dimension of the harmonic measure, the asymptotic entro...

Ausführliche Beschreibung

Bibliographische Detailangaben
Veröffentlicht in:	Transactions of the American Mathematical Society. - American Mathematical Society, 1900. - 359(2007), 6, Seite 2881-2898
1. Verfasser:	Le Prince, Vincent (VerfasserIn)
Format:	Online-Aufsatz
Sprache:	English
Veröffentlicht:	2007
Zugriff auf das übergeordnete Werk:	Transactions of the American Mathematical Society
Schlagworte:	Ergodic theory random walk hyperbolic group harmonic measure entropy Mathematics Physical sciences Philosophy Applied sciences


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245	1	0	\|a Dimensional Properties of the Harmonic Measure for a Random Walk on a Hyperbolic Group
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520			\|a This paper deals with random walks on isometry groups of Gromov hyperbolic spaces, and more precisely with the dimension of the harmonic measure ν associated with such a random walk. We first establish a link of the form dim ν ≤ h/l between the dimension of the harmonic measure, the asymptotic entropy h of the random walk and its rate of escape l. Then we use this inequality to show that the dimension of this measure can be made arbitrarily small and deduce a result on the type of the harmonic measure.
540			\|a Copyright 2007 American Mathematical Society
650		4	\|a Ergodic theory
650		4	\|a random walk
650		4	\|a hyperbolic group
650		4	\|a harmonic measure
650		4	\|a entropy
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Random walk
650		4	\|a Mathematics
650		4	\|a Physical sciences \|x Physics \|x Thermodynamics \|x Thermodynamic properties \|x Entropy
650		4	\|a Philosophy \|x Logic \|x Logical topics \|x Formal logic \|x Mathematical logic \|x Mathematical set theory \|x Transfinite numbers \|x Infinity
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Statistical physics \|x Dimensional analysis \|x Dimensionality \|x Abstract spaces \|x Hausdorff dimensions
650		4	\|a Mathematics \|x Mathematical analysis \|x Measure theory \|x Hausdorff measures
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Descriptive statistics \|x Statistical distributions \|x Distribution functions \|x Probability distributions \|x Mathematical moments
650		4	\|a Physical sciences \|x Physics \|x Mechanics \|x Classical mechanics \|x Kinematics \|x Trajectories
650		4	\|a Applied sciences \|x Systems science \|x Systems theory \|x Dynamical systems \|x Ergodic theory
655		4	\|a research-article
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