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Gaussian upper bounds for heat kernels of continuous time simple random walks. (English) Zbl 1244.60099
Summary: We consider continuous time simple random walks with arbitrary speed measure \(\theta\) on infinite weighted graphs. Write \(p_t(x,y)\) for the heat kernel of this process. Given on-diagonal upper bounds for the heat kernel at two points \(x_1,x_2\), we obtain a Gaussian upper bound for \(p_t(x_1,x_2)\). The distance function which appears in this estimate is not in general the graph metric, but a new metric which is adapted to the random walk. Long-range non-Gaussian bounds in this new metric are also established. Applications to heat kernel bounds for various models of random walks in random environments are discussed.

60K37 Processes in random environments
60G50 Sums of independent random variables; random walks
35K08 Heat kernel
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