Cycle density in infinite Ramanujan graphs

Russell Lyons, Yuval Peres

Type: Article

Publication Date: 2015-11-01

Citations: 7

DOI: https://doi.org/10.1214/14-aop961

View Publication

Locations

The Annals of Probability - View
arXiv (Cornell University) - View - PDF
Project Euclid (Cornell University) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Kesten’s theorem for uniformly recurrent subgroups	2019	Mikołaj Frączyk
+ PDF Chat	Bounded Cutoff Window for the Non-backtracking Random Walk on Ramanujan Graphs	2023	Evita Nestoridi Peter Sarnak
+	Bounded cutoff window for the non-backtracking random walk on Ramanujan Graphs	2021	Evita Nestoridi Peter Sarnak
+	Eigenvalues of Non-Backtracking Walks in a Cycle with Random Loops	2007	Ana-Roxana Pop
+	Random walks, spectral radii, and Ramanujan graphs	2004	Tatiana Nagnibeda
+ PDF Chat	Short Cycles in Random Regular Graphs	2004	Brendan D. McKay Nicholas Wormald Beata Wysocka
+	The measurable Kesten theorem	2016	Miklós Abért Yair Glasner Bálint Virág
+ PDF Chat	Cutoff on all Ramanujan graphs	2016	Eyal Lubetzky Yuval Peres
+	Kesten's theorem for uniformly recurrent subgroups	2018	Mikołaj Frączyk
+	Kesten's theorem for uniformly recurrent subgroups	2018	Mikołaj Frączyk
+	Cycles in random graphs and hypergraphs	1992	V. F. Kolchin
+	Cutoff on all Ramanujan graphs	2015	Eyal Lubetzky Yuval Peres
+	Cutoff on all Ramanujan graphs	2015	Eyal Lubetzky Yuval Peres
+ PDF Chat	A random walk among random graphs	2024	Nicolas Curien
+	Random walks on random regular simple graphs	1994	Martin Hildebrand
+	Cutoff for Ramanujan graphs via degree inflation	2017	Jonathan Hermon
+	Random Walks on Random Graphs	2012	Colin Cooper Alan Frieze
+ PDF Chat	Periodic Walks on Large Regular Graphs and Random Matrix Theory	2014	Idan Oren Uzy Smilansky
+	Random walks, spectral radii, and Ramanujan graphs	2004	Tatiana Nagnibeda
+	Random Walks on Finite Graphs	2024	Rinaldo B. Schinazi

Works That Cite This (6)

Action	Title	Year	Authors
+	The measurable Kesten theorem	2016	Miklós Abért Yair Glasner Bálint Virág
+	Sharp ellipticity conditions for ballistic behavior of random walks in random environment	2015	Élodie Bouchet Alejandro F. Ramı́rez Christophe Sabot
+ PDF Chat	Invariant random subgroups of linear groups	2017	Yair Glasner
+	Invariant random subgroups of linear groups	2014	Tsachik Gelander Yair Glasner
+	Generic IRS in free groups, after Bowen	2014	Amichai Eisenmann Yair Glasner
+ PDF Chat	Kesten’s theorem for uniformly recurrent subgroups	2019	Mikołaj Frączyk

Works Cited by This (19)

Action	Title	Year	Authors
+	A Lower Bound for the Smallest Eigenvalue of the Laplacian	2015	Jeff Cheeger
+	Probability on Trees and Networks	2016	Russell Lyons Yuval Peres
+ PDF Chat	Eigenvalues and expanders	1986	Ilan Alon
+	Dirichlet norms, capacities and generalized isoperimetric inequalities for Markov operators	1992	Vadim A. Kaimanovich
+	Symmetric random walks on groups	1959	Harry Kesten
+	Random walks on graphs with a strong isoperimetric property	1988	Peter Gerl
+	On the second eigenvalue of a graph	1991	A. Nilli
+ PDF Chat	Difference equations, isoperimetric inequality and transience of certain random walks	1984	Józef Dodziuk
+	The Spectral Radius of infinite Graphs	1988	N. L. Biggs Bojan Mohar John Shawe‐Taylor
+	Isoperimetric inequalities and Markov chains	1985	N. Th. Varopoulos