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 Electronic Journal of Probability > Vol. 12 (2007) > Paper 1 open journal systems 


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.


Full text: PDF

Pages: 1-46

Published on: January 14, 2007
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Electronic Journal of Probability. ISSN: 1083-6489