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Geometric structures of late points of a two-dimensional simple random walk. (English) Zbl 1448.60028
Summary: As A. Dembo [Lect. Notes Math. 1869, 5–101 (2005; Zbl 1102.60009); in: Proceedings of the international congress of mathematicians (ICM), Spain, 2006. Volume III: Invited lectures. Zürich: European Mathematical Society (EMS). 535–558 (2006; Zbl 1099.60028)] suggested, we consider the problem of late points for a simple random walk in two dimensions. It has been shown that the exponents for the number of pairs of late points coincide with those of favorite points and high points in the Gaussian free field, whose exact values are known. We determine the exponents for the number of \(j\)-tuples of late points on average.

60D05 Geometric probability and stochastic geometry
60G50 Sums of independent random variables; random walks
60J55 Local time and additive functionals
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