TY - JOUR
T1 - Heat kernel estimates for strongly recurrent random walk on random media
AU - Kumagai, Takashi
AU - Misumi, Jun
N1 - Funding Information:
J. Misumi research partially supported by the 21 century COE program at Graduate School of Mathematical Sciences, the University of Tokyo.
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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U2 - 10.1007/s10959-008-0183-5
DO - 10.1007/s10959-008-0183-5
M3 - Article
AN - SCOPUS:54149108750
SN - 0894-9840
VL - 21
SP - 910
EP - 935
JO - Journal of Theoretical Probability
JF - Journal of Theoretical Probability
IS - 4
ER -