Frequent points for random walks in two dimensions
Richard F. Bass, University of Connecticut
Jay Rosen, College of Staten Island, CUNY
Abstract
For a symmetric random walk in Z2 which does not necessarily
have bounded jumps we study those points which are visited an
unusually large number of times. We prove the analogue of the
Erdös-Taylor conjecture and obtain the asymptotics for the number of
visits to the most visited site. We also obtain the asymptotics for
the number of points which are visited very frequently by time n.
Among the tools we use are Harnack inequalities and Green's function
estimates for random walks with unbounded jumps; some of these are of
independent interest.
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