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Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps
, 2008
"... We investigate the relationships between the parabolic Harnack inequality, heat kernel estimates, some geometric conditions, and some analytic conditions for random walks with long range jumps. Unlike the case of diffusion processes, the parabolic Harnack inequality does not, in general, imply the c ..."
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Cited by 8 (6 self)
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We investigate the relationships between the parabolic Harnack inequality, heat kernel estimates, some geometric conditions, and some analytic conditions for random walks with long range jumps. Unlike the case of diffusion processes, the parabolic Harnack inequality does not, in general, imply the corresponding heat kernel estimates.
The Einstein relation for random walks on graphs
, 2008
"... This paper investigates the Einstein relation; the connection between the volume growth, the resistance growth and the expected time a random walk needs to leave a ball on a weighted graph. The Einstein relation is proved under different set of conditions. In the simplest case it is shown under the ..."
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Cited by 2 (1 self)
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This paper investigates the Einstein relation; the connection between the volume growth, the resistance growth and the expected time a random walk needs to leave a ball on a weighted graph. The Einstein relation is proved under different set of conditions. In the simplest case it is shown under the volume doubling and time comparison principles. This and the other set of conditions provide the basic vwork for the study of (sub) diffusive behavior of the random walks on weighted graphs. 1
GREEN KERNEL ESTIMATES AND THE FULL MARTIN BOUNDARY FOR RANDOM WALKS ON LAMPLIGHTER GROUPS AND DIESTELLEADER GRAPHS
, 2004
"... Abstract. We determine the precise asymptotic behaviour (in space) of the Green kernel of simple random walk with drift on the DiestelLeader graph DL(q, r), where q, r ≥ 2. The latter is the horocyclic product of two homogeneous trees with respective degrees q + 1 and r + 1. When q = r, it is the C ..."
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Abstract. We determine the precise asymptotic behaviour (in space) of the Green kernel of simple random walk with drift on the DiestelLeader graph DL(q, r), where q, r ≥ 2. The latter is the horocyclic product of two homogeneous trees with respective degrees q + 1 and r + 1. When q = r, it is the Cayley graph of the wreath product (lamplighter group) Zq ≀ Z with respect to a natural set of generators. We describe the full Martin compactification of these random walks on DLgraphs and, in particular, lamplighter groups. This completes and provides a better approach to previous results of Woess, who has determined all minimal positive harmonic functions. 1.
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"... www.imstat.org/aihp Random walk on graphs with regular resistance and volume growth ..."
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www.imstat.org/aihp Random walk on graphs with regular resistance and volume growth