Heat kernel estimates for strongly recurrent random walk on random media

Takashi Kumagai; Jun Misumi

doi:10.1007/s10959-008-0183-5

Heat kernel estimates for strongly recurrent random walk on random media

Takashi Kumagai^*, Jun Misumi

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

35 Citations (Scopus)

Abstract

We establish general estimates for simple random walk on an arbitrary infinite random graph, assuming suitable bounds on volume and effective resistance for the graph. These are generalizations of the results in Barlow et al. (Commun. Math. Phys. 278:385-431, 2008, Sects. 1, 2) and in particular imply the spectral dimension of the random graph. We will also give an application of the results to random walk on a long-range percolation cluster.

Original language	English
Pages (from-to)	910-935
Number of pages	26
Journal	Journal of Theoretical Probability
Volume	21
Issue number	4
DOIs	https://doi.org/10.1007/s10959-008-0183-5
Publication status	Published - 2008 Dec
Externally published	Yes

Keywords

Heat kernel estimates
Long-range percolation
Random media
Random walk
Spectral dimension

ASJC Scopus subject areas

Statistics and Probability
Mathematics(all)
Statistics, Probability and Uncertainty

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10.1007/s10959-008-0183-5

Cite this

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title = "Heat kernel estimates for strongly recurrent random walk on random media",

abstract = "We establish general estimates for simple random walk on an arbitrary infinite random graph, assuming suitable bounds on volume and effective resistance for the graph. These are generalizations of the results in Barlow et al. (Commun. Math. Phys. 278:385-431, 2008, Sects. 1, 2) and in particular imply the spectral dimension of the random graph. We will also give an application of the results to random walk on a long-range percolation cluster.",

keywords = "Heat kernel estimates, Long-range percolation, Random media, Random walk, Spectral dimension",

author = "Takashi Kumagai and Jun Misumi",

note = "Funding Information: J. Misumi research partially supported by the 21 century COE program at Graduate School of Mathematical Sciences, the University of Tokyo.",

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language = "English",

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AU - Misumi, Jun

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PY - 2008/12

Y1 - 2008/12

N2 - We establish general estimates for simple random walk on an arbitrary infinite random graph, assuming suitable bounds on volume and effective resistance for the graph. These are generalizations of the results in Barlow et al. (Commun. Math. Phys. 278:385-431, 2008, Sects. 1, 2) and in particular imply the spectral dimension of the random graph. We will also give an application of the results to random walk on a long-range percolation cluster.

AB - We establish general estimates for simple random walk on an arbitrary infinite random graph, assuming suitable bounds on volume and effective resistance for the graph. These are generalizations of the results in Barlow et al. (Commun. Math. Phys. 278:385-431, 2008, Sects. 1, 2) and in particular imply the spectral dimension of the random graph. We will also give an application of the results to random walk on a long-range percolation cluster.

KW - Heat kernel estimates

KW - Long-range percolation

KW - Random media

KW - Random walk

KW - Spectral dimension

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Heat kernel estimates for strongly recurrent random walk on random media

Abstract

Keywords

ASJC Scopus subject areas

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