Vertex-reinfoced random walk on Z visits finitely many states

Details Vertex-reinfoced random walk on Z visits finitely many states Vertex-reinfoced random walk on Z visits finitely many states

1997-01-23

arxiv.org/abs/math/9701224v1

Mathematics

Probability

Scientific paper

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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