Tohoku Mathematical Journal
2005
December
SECOND SERIES VOL. 57, NO. 4

Tohoku Math. J.
57 (2005), 559-587

Title THE DISCRETE INTEGRAL MAXIMUM PRINCIPLE AND ITS APPLICATIONS

Author Thierry Coulhon, Alexander Grigor'yan and Fabio Zucca

(Received December 3, 2003)
Abstract. We prove an integral maximum principle for random walks on graphs, and give several applications to pointwise estimates of their transition probabilities, including the time-dependent case.

2000 Mathematics Subject Classification. Primary 60J15; Secondary 35B50, 39A12.
Key words and phrases. Discrete integral maximum principle, random walks on graphs, upper and lower estimates for a discrete heat kernel, time-dependent random walks, random walks on percolation clusters.

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