Woess, Wolfgang; matematični kolokvij april 2001

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Random walks on infinite graphs

Wolfgang Woess

Tehniška Univerza v Gradcu, Avstrija

19. april 2001

Let X be a locally finite, infinite, connected graph. The Simple Random Walk on X is the random process where a random walker performs successive steps along the graph's edges; at each site (vertex) he chooses with equal probability one among the neighbouring sites to which he will move next. The general theme of the talk will be the interplay between geometry (the structure of the underlying graph) and probability (stochastic properties of the random walk). For example, Polya (1921) has shown that the Simple Random Walk on the integer grid is recurrent in dimensions 1 and 2 (the walker returns almost surely to the starting point) and transient in bigger dimensions (the walker wanders off to infinity). Which structural features stand behind this phenomenon? In the talk, a few questions and answers of this type will be reviewed.

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