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2007 Frequent Points for Random Walks in Two Dimensions
Richard Bass, Jay Rosen
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Electron. J. Probab. 12: 1-46 (2007). DOI: 10.1214/EJP.v12-388


For a symmetric random walk in $Z^2$ 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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Richard Bass. Jay Rosen. "Frequent Points for Random Walks in Two Dimensions." Electron. J. Probab. 12 1 - 46, 2007.


Accepted: 14 January 2007; Published: 2007
First available in Project Euclid: 1 June 2016

zbMATH: 1127.60042
MathSciNet: MR2280257
Digital Object Identifier: 10.1214/EJP.v12-388

Primary: 60G50
Secondary: 60F15

Keywords: frequent points , Green's functions , Harnack inequalities , Random walks

Vol.12 • 2007
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