The Liouville and the intersection properties are equivalent for planar graphs

Itaı Benjamini, Nicolas Curien, Agelos Georgakopoulos

Type: Preprint

Publication Date: 2012-01-01

Citations: 0

DOI: https://doi.org/10.48550/arxiv.1203.4002

View Publication

Locations

arXiv (Cornell University) - View - PDF
Warwick Research Archive Portal (University of Warwick) - View - PDF
Project Euclid (Cornell University) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	The Liouville and the intersection properties are equivalent for planar graphs	2012	Itaı Benjamini Nicolas Curien Agelos Georgakopoulos
+ PDF Chat	Geodesics and Bounded Harmonic Functions on Infinite Planar Graphs	1991	S. Northshield
+ PDF Chat	Geodesics and bounded harmonic functions on infinite planar graphs	1991	S. Northshield
+	Equivalence of zero entropy and the Liouville property for stationary random graphs	2015	Matías Piaggio Pablo Lessa
+	Equivalence of zero entropy and the Liouville property for stationary random graphs	2015	Matías Piaggio Pablo Lessa
+	Behaviour at Infinity and Harmonic Functions of Random Walks on Graphs	1991	Wolfgang Woess
+	Equivalence of zero entropy and the Liouville property for stationary random graphs	2016	Matías Piaggio Pablo Lessa
+	A strong Liouville theorem for $p$-harmonic functions on graphs	1997	Ilkka Holopainen Paolo M. Soardi
+	Liouville property and non-negative Ollivier curvature on graphs	2019	Jürgen Jost Florentin Münch Christian Rose
+ PDF Chat	Existence of the Harmonic Measure for Random Walks on Graphs and in Random Environments	2013	Daniel Boivin Clément Rau
+ PDF Chat	Random walks and harmonic functions on infinite planar graphs using square tilings	1996	Itaı Benjamini Oded Schramm
+	Intersection Properties of Simple Random Walks: A Renormalization Group Approach	1985	Giovanni Felder Jürg Fröhlich
+	Intersections of Random Walks (Gregory F. Lawler)	1992	Richard Durrett
+	Random walks and isoperimetric inequalities on infinite planar graphs and their duals = 無限平面グラフにおける酔歩と等周不等式	1995	雄介樋口
+	Polyharmonic Functions for Finite Graphs and Markov Chains	2020	Thomas Hirschler Wolfgang Woess
+	Bounded Harmonic functions	2024
+	Harmonic Functions and Random Walks on Spheres	2013	Annie Brunelle Emily Diana Jeffrey Dzugan Ryan Gallagher Elisabeth Johnson David Wegscheid И.Н. Назаров
+ PDF Chat	Kato’s inequality and Liouville theorems on locally finite graphs	2013	Li Ma Xiang-Yang Wang
+	Intersections of Random Walks	2012	Gregory F. Lawler
+	Intersections of simple random walks	1985	Gregory F. Lawler

Works That Cite This (0)

Action	Title	Year	Authors

Works Cited by This (6)

Action	Title	Year	Authors
+	Local structure of random quadrangulations	2005	Maxim Krikun
+	3-connected planar spaces uniquely embed in the sphere	2002	R. Bruce Richter Carsten Thomassen
+	Harmonic functions on planar and almost planar graphs and manifolds, via circle packings	1996	Itaı Benjamini Oded Schramm
+ PDF Chat	Ergodic theory on stationary random graphs	2012	Itaı Benjamini Nicolas Curien
+	Lack of Sphere Packing of Graphs via Non-Linear Potential Theory	2009	Itaı Benjamini Oded Schramm
+ PDF Chat	LACK OF SPHERE PACKING OF GRAPHS VIA NONLINEAR POTENTIAL THEORY	2013	Itaı Benjamini Oded Schramm