Gaussian upper bounds for heat kernels of continuous time simple random walks

Details Gaussian upper bounds for heat kernels of continuous time simple random walks Gaussian upper bounds for heat kernels of continuous time simple random walks

2011-02-11

arxiv.org/abs/1102.2265v2

M. Folz. Gaussian upper bounds for heat kernels of continuous time simple random walks on graphs. Elec. J. Prob. 62 (2011), 16

Mathematics

Probability

Corrected misprints and typos, updated references

Scientific paper

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.

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