Vertex-reinfoced random walk on Z visits finitely many states
Robin Pemantle, Stanislav Volkov
Abstract
Vertex-reinforced random walk is defined in Pemantle's (1988) thesis; it is a random walk that is biased to visit sites it has already visited a lot. We show that this reinforcement scheme, in contrast to the scheme of edge-reinforcement, causes random walk on a line to get trapped in a finite set.
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