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Sub-Gaussian estimates of heat kernels on infinite graphs
- Duke Math. J
, 2000
"... We prove that a two sided sub-Gaussian estimate of the heat kernel on an infinite weighted graph takes place if and only if the volume growth of the graph is uniformly polynomial and the Green kernel admits a uniform polynomial decay. ..."
Abstract
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Cited by 27 (8 self)
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We prove that a two sided sub-Gaussian estimate of the heat kernel on an infinite weighted graph takes place if and only if the volume growth of the graph is uniformly polynomial and the Green kernel admits a uniform polynomial decay.
Manifolds and Graphs With Slow Heat Kernel Decay
- Invent. Math
, 1999
"... We give upper estimates on the long time behaviour of the heat kernel on a non-compact Riemannian manifold and infinite graphs, which only depend on a lower bound of the volume growth. We also show that these estimates are optimal. ..."
Abstract
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Cited by 19 (2 self)
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We give upper estimates on the long time behaviour of the heat kernel on a non-compact Riemannian manifold and infinite graphs, which only depend on a lower bound of the volume growth. We also show that these estimates are optimal.
Large time behavior of the heat kernel
, 2002
"... In this paper we study the large time behavior of the (minimal) heat kernel kM P (x, y, t) of a general time independent parabolic operator L = ut+P(x, ∂x) which is defined on a noncompact manifold M. More precisely, we prove that lim t→ ∞ eλ0t k M P (x, y, t) always exists. Here λ0 is the generaliz ..."
Abstract
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Cited by 5 (2 self)
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In this paper we study the large time behavior of the (minimal) heat kernel kM P (x, y, t) of a general time independent parabolic operator L = ut+P(x, ∂x) which is defined on a noncompact manifold M. More precisely, we prove that lim t→ ∞ eλ0t k M P (x, y, t) always exists. Here λ0 is the generalized principal eigenvalue of the operator P in M.
