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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
frequent points
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