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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.

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