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A random walk proof of the Erdős-Taylor conjecture. (English) Zbl 1098.60045
In A. Dembo, Y. Peres, J. Rosen and O. Zeitouni [Acta. Math. 186, No. 2, 239–270 (2001; Zbl 1008.60063)], the Erdős-Taylor conjecture, concerning the asymptotics of the number of visits to the most frequently visited point in the first \(n\) steps of the simple planar random walk. Their proof was by deduction from a related result for planar Brownian motion. In this paper, the conjecture, together with some refinements, is proved by purely random walk arguments.

MSC:
60G50 Sums of independent random variables; random walks
Keywords:
frequent points
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