Ergodic theory on Galton—Watson trees: speed of random walk and dimension of harmonic measure

Russell Lyons, Robin Pemantle, Yuval Peres

Type: Article

Publication Date: 1995-06-01

Citations: 172

DOI: https://doi.org/10.1017/s0143385700008543

View Publication

Locations

Ergodic Theory and Dynamical Systems - View

Similar Works

Action	Title	Year	Authors
+	How Fast and where does a Random Walker Move on a Random Tree?	1996	Russell Lyons
+ PDF Chat	Tree-indexed random walk and random walk on trees	2014	Shen Lin
+	Invariant measures, Hausdorff dimension and dimension drop of some harmonic measures on Galton-Watson trees	2018	Pierre Rousselin
+	Harmonic measure for biased random walk in a supercritical Galton-Watson tree	2017	Shen Lin
+	Invariant Measures, Hausdorff Dimension and Dimension Drop of some Harmonic Measures on Galton-Watson Trees	2017	Pierre Rousselin
+	Invariant Measures, Hausdorff Dimension and Dimension Drop of some Harmonic Measures on Galton-Watson Trees	2017	Pierre Rousselin
+ PDF Chat	Harmonic measure for biased random walk in a supercritical Galton–Watson tree	2019	Shen Lin
+	The harmonic measure of balls in random trees	2017	Nicolas Curien Jean‐François Le Gall
+ PDF Chat	Dimension Drop for Transient Random Walks on Galton-Watson Trees in Random Environments	2023	Pierre Rousselin
+	Dimension Drop for Transient Random Walks on Galton-Watson Trees in Random Environments	2017	Pierre Rousselin
+ PDF Chat	Biased random walks on Galton–Watson trees	1996	Russell Lyons Robin Pemantle Yuval Peres
+	Hausdorff dimension of the harmonic measure on trees	1998	Vadim A. Kaimanovich
+	Typical behavior of the harmonic measure in critical Galton-Watson trees	2015	Shen Lin
+	The harmonic measure of balls in critical Galton-Watson trees with infinite variance offspring distribution	2014	Shen Lin
+	Typical behavior of the harmonic measure in critical Galton-Watson trees with infinite variance offspring distribution	2016	Shen Lin
+ PDF Chat	The harmonic measure of balls in critical Galton-Watson trees with infinite variance offspring distribution	2014	Shen Lin
+ PDF Chat	Typical Behavior of the Harmonic Measure in Critical Galton–Watson Trees with Infinite Variance Offspring Distribution	2017	Shen Lin
+ PDF Chat	On the speed of random walks on graphs	2000	Bálint Virág
+	Invariance and attraction properties of Galton-Watson trees	2019	Yevgeniy Kovchegov Ilya Zaliapin
+	Invariance and attraction properties of Galton-Watson trees	2019	Yevgeniy Kovchegov Ilya Zaliapin

Works That Cite This (171)

Action	Title	Year	Authors
+	Disorder, entropy and harmonic functions	2015	Itaı Benjamini Hugo Duminil‐Copin Gady Kozma Ariel Yadin
+ PDF Chat	Coarse Geometry and Randomness	2013	Itaı Benjamini
+	The potential energy of biased random walks on trees	2014	Yueyun Hu Zhan Shi
+	Wired cycle-breaking dynamics for uniform spanning forests	2016	Tom Hutchcroft
+	On transience of frogs on Galton–Watson trees	2020	Sebastian Müller Gundelinde Maria Wiegel
+	Reversible Markov Chains and Random Walks on Graphs	2014	David Aldous James Allen Fill
+ PDF Chat	Processes on Unimodular Random Networks	2007	David Aldous Russell Lyons
+ PDF Chat	Ergodic theory on stationary random graphs	2012	Itaı Benjamini Nicolas Curien
+ PDF Chat	Einstein relation for biased random walk on Galton–Watson trees	2013	Gérard Ben Arous Yueyun Hu Stefano Olla Ofer Zeitouni
+ PDF Chat	Large deviations for random walk in random environment with holding times	2004	Amir Dembo Nina Gantert Ofer Zeitouni

Works Cited by This (16)

Action	Title	Year	Authors
+	On the Distortion of Boundary Sets Under Conformal Mappings	1985	Nikolai Makarov
+ PDF Chat	Random Walks and Percolation on Trees	1990	Russell Lyons
+ PDF Chat	Random Walks in a Random Environment	1975	Fred Solomon
+ PDF Chat	Hausdorff dimension of harmonic measures on negatively curved manifolds	1990	Yuri Kifer François Ledrappier
+ PDF Chat	Dimension, entropy and Lyapunov exponents	1982	Lai-Sang Young
+	Trees Generated by a Simple Branching Process	1981	John Hawkes
+	A note on a functional equation arising in Galton-Watson branching processes	1971	Krishna B. Athreya
+	Exact distributions of kin numbers in a Galton-Watson process	1982	A. Joffe W. A. O’N. Waugh
+	Subdiffusive behavior of random walk on a random cluster	1986	Harry Kesten
+	Ergodic Theory	1982	I. P. Cornfeld Ya. G. Sinaĭ Sergey Fomin