Gaussian lower bounds for random walks from elliptic regularity

Pascal Auscher, Thierry Coulhon

Type: Article

Publication Date: 1999-09-01

Citations: 24

DOI: https://doi.org/10.1016/s0246-0203(99)00109-0

Abstract

We give a direct approach to off-diagonal lower bounds for reversible Markov chains on infinite graphs with regular volume growth and Poincaré inequalities, by using ideas that go back to De Giorgi and Morrey.

Locations

Annales de l Institut Henri Poincaré Probabilités et Statistiques - View
French digital mathematics library (Numdam) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Properties of random walks on discrete groups: Time regularity and off-diagonal estimates	2007	Nick Dungey
+	On diagonal lower bound of Markov kernel from $L^2$ analyticity	2015	Joseph Feneuil
+	ON SPECTRAL BOUNDS FOR SYMMETRIC MARKOV CHAINS WITH COARSE RICCI CURVATURES (確率論シンポジウム : RIMS研究集会報告集)	2013	一洋桑江
+	Random walks on graphs with volume and time doubling	2008	András Telcs
+ PDF Chat	Random walks on graphs with volume and time doubling	2006	András Telcs
+ PDF Chat	Minorations pour les chaînes de Markov unidimensionnelles	1993	Thierry Coulhon Laurent Saloff‐Coste
+	Heat Kernel Estimates on Simple Random Walks and On-Diagonal Upper Bounds	2024	Runquan Zuo Yunfei Yan Zhibo Zhu Liqiang Yao Qing‐Long Han
+	Entropic Ricci curvature bounds for discrete interacting systems	2016	Max Fathi Jan Maas
+ PDF Chat	Geometric Bounds for Eigenvalues of Markov Chains	1991	Persi Diaconis Daniel W. Stroock
+	Lower bounds for covering times for reversible Markov chains and random walks on graphs	1989	David Aldous
+	Characterization of sub-Gaussian heat kernel estimates on strongly recurrent graphs	2005	Martin T. Barlow Thierry Coulhoun Takashi Kumagai
+ PDF Chat	Local Sub-Gaussian Estimates on Graphs: The Strongly Recurrent Case	2001	András Telcs
+	On Sidorenko's conjecture for determinants and Gaussian Markov random fields	2017	Balázs Szegedy
+	Ollivier Ricci curvature for general graph Laplacians: Heat equation, Laplacian comparison, non-explosion and diameter bounds	2019	Florentin Münch Radosław K. Wojciechowski
+	Ollivier Ricci curvature for general graph Laplacians: Heat equation, Laplacian comparison, non-explosion and diameter bounds	2017	Florentin Münch Radosław K. Wojciechowski
+	Ollivier Ricci curvature for general graph Laplacians: Heat equation, Laplacian comparison, non-explosion and diameter bounds	2017	Florentin Münch Radosław K. Wojciechowski
+	Random Walks and Heat Kernels on Graphs	2017	Martin T. Barlow
+	Harnack inequalities and sub-Gaussian estimates for random walks	2002	Alexander Grigor’yan András Telcs
+	Random Walks on Graphs with Regular Volume Growth	1998	Thierry Coulhon Alexander Grigor’yan
+ PDF Chat	Gaussian Estimates for Markov Chains and Random Walks on Groups	1993	Waldemar Hebisch L. Saloff-Coste

Works That Cite This (22)

Action	Title	Year	Authors
+	Gaussian heat kernel bounds through elliptic Moser iteration	2016	Frédéric Bernicot Thierry Coulhon Dorothee Frey
+	Li-Yau inequality on graphs	2015	Frank Bauer Paul Horn Yong Lin Gábor Lippner Dan Mangoubi Shing‐Tung Yau
+ PDF Chat	RACINES CARRÉES D'OPÉRATEURS ELLIPTIQUES ET ESPACES DE HARDY	2011	Emmanuel Russ
+ PDF Chat	$H^1$-BMO duality on graphs	2000	Emmanuel Russ
+	Divergence Form Operators on Fractal-like Domains	2000	Martin T. Barlow Richard F. Bass
+ PDF Chat	Interpolation réelle des espaces de Sobolev sur les espaces métriques mesurés et applications aux inégalités fonctionnelles	2007	Nadine Badr
+	Moser–Nash kernel estimates for degenerate parabolic equations	2016	Verena Bögelein F. Ragnedda Stella Vernier Piro Vincenzo Vesprı
+	Regularity of quasi-minimizers on metric spaces	2001	Juha Kinnunen Nageswari Shanmugalingam
+	Geometric Interpretations of LP-Poincar� Inequalities on Graphs with Polynomial Volume Growth	2004	Thierry Coulhon Pekka Koskela
+ PDF Chat	Sub-Gaussian estimates of heat kernels on infinite graphs	2001	Alexander Grigor’yan András Telcs

Works Cited by This (0)

Action	Title	Year	Authors