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Gaussian Upper Bounds for Heat Kernels of Continuous Time Simple Random Walks

   
@article{EJP926,
	author = {Matthew Folz},
	title = {Gaussian Upper Bounds for Heat Kernels of Continuous Time Simple Random Walks},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {16},
	year = {2011},
	keywords = {random walk; heat kernel; Gaussian upper bound; random walk in random environment},
	abstract = {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.},
	pages = {no. 62, 1693-1722},
	issn = {1083-6489},
	doi = {10.1214/EJP.v16-926},    
        url = {http://ejp.ejpecp.org/article/view/926}}