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Heat kernels of graphs. (English) Zbl 0799.58085

We prove a sharper pointwise upper bound for the heat kernel of the continuous time random walk on a general graph under a weaker assumption than that by I. Chavel and E. A. Feldman in ‘Modified isoperimetric constants and large time heat diffusion in Riemannian manifolds’, preprint 1990. Our main result is stated in Theorem 2.6. Our approach is a discrete version of the method first developed by E. B. Davies in Am. J. Math. 109, 319-333 (1987; Zbl 0659.35009) for obtaining Gaussian upper bounds for heat kernels of elliptic operators on manifolds.

MSC:

58J99 Partial differential equations on manifolds; differential operators
39A12 Discrete version of topics in analysis
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