Heat kernel estimates and parabolic Harnack inequalities on graphs and resistance forms
type: Item
instance of: scholarly article
title: Heat kernel estimates and parabolic Harnack inequalities on graphs and resistance forms
zbMATH Open document ID: 1067.60070
author: Takashi Kumagai
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2005-04-04T00:00:00Z
review text: This paper is an invited contribution to the special issue of Publications of RIMS. It presents recent work (partly published at that time only in preprint form) of the author and also joint work of the author with R. F. Bass, M. T. Barlow, T. Coulhon. The framework for the main result is that of a measure metric space, on which a resistance form, as defined by \textit{J. Kigami} [``Analysis on fractals'' (2001; Zbl 0998.28004)] is given. With this resistance form, one associates a heat kernel. The main result asserts the equivalence between a form of upper and lower estimate for the heat kernel, and a uniform volume growth with volume doubling condition. Examples (on trees and fractals), where such upper or lower estimates hold are presented in a final chapter.
reviewed by: Liliana Popa
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 2151103
zbMATH Keywords: uniform volume growth
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1145475493
OpenAlex ID: W2092586214
cites work: Bounds for the fundamental solution of a parabolic equation
cites work: Which values of the volume growth and escape time exponent are possible for a graph?
cites work: Q4453420
cites work: Q3160531
cites work: Brownian Motion and Harmonic Analysis on Sierpinski Carpets
cites work: Stability of parabolic Harnack inequalities
cites work: Stability of parabolic Harnack inequalities on metric measure spaces
cites work: Manifolds and graphs with slow heat kernel decay
cites work: Characterization of sub‐Gaussian heat kernel estimates on strongly recurrent graphs
cites work: Diffusions and Elliptic Operators
cites work: A Saint-Venant type principle for Dirichlet forms on discontinuous media
cites work: OFF-DIAGONAL HEAT KERNEL LOWER BOUNDS WITHOUT POINCARÉ
cites work: Lower bounds for one-dimensional Markov chains
cites work: Isometric Riemannian manifolds at infinity
cites work: Q4041031
cites work: Parabolic Harnack inequality and estimates of Markov chains on graphs
cites work: A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash
cites work: Transition density estimates for Brownian motion on affine nested fractals
cites work: Dirichlet forms and symmetric Markov processes
cites work: Sub-Gaussian estimates of heat kernels on infinite graphs
cites work: Harnack inequalities and sub-Gaussian estimates for random walks
cites work: Transition Density Estimates for Diffusion Processes on Post Critically Finite Self-Similar Fractals
cites work: Q4664798
cites work: On the relation between elliptic and parabolic Harnack inequalities
cites work: Transition probabilities for the simple random walk on the Sierpinski graph
cites work: Rough isometries, and combinatorial approximations of geometries of non- compact Riemannian manifolds
cites work: Q3723243
cites work: Harmonic calculus on limits of networks and its application to dendrites
cites work: Analysis on fractals
cites work: Harmonic analysis for resistance forms.
cites work: Estimates of transition densities for Brownian motion of nested fractals
cites work: Q4266172
DOI: 10.2977/PRIMS/1145475493
description: scientific article; zbMATH DE number 2151103