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math.PR1997
Vertex-reinfoced random walk on Z visits finitely many states
Robin Pemantle, Stanislav Volkov
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 reinforcemen…
math.PR1997★ 1 cited
Markov chains in a field of traps
Robin Pemantle, Stanislav Volkov
A general criterion is given for when a Markov chain trapped with probability p(x) in state x will be almost surely trapped. The quenched (state x is a trap forever with probabilit…