Annals of Probability

Geometric structures of late points of a two-dimensional simple random walk

Izumi Okada

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Abstract

As Dembo (In Lectures on Probability Theory and Statistics (2005) 1–101 Springer, and International Congress of Mathematicians, Vol. III (2006) 535–558, Eur. Math. Soc.) 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.

Article information

Source
Ann. Probab., Volume 47, Number 5 (2019), 2869-2893.

Dates
Received: March 2018
Revised: November 2018
First available in Project Euclid: 22 October 2019

Permanent link to this document
https://projecteuclid.org/euclid.aop/1571731439

Digital Object Identifier
doi:10.1214/18-AOP1325

Mathematical Reviews number (MathSciNet)
MR4021239

Zentralblatt MATH identifier
07145305

Subjects
Primary: 60G60: Random fields
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Local time late point simple random walks

Citation

Okada, Izumi. Geometric structures of late points of a two-dimensional simple random walk. Ann. Probab. 47 (2019), no. 5, 2869--2893. doi:10.1214/18-AOP1325. https://projecteuclid.org/euclid.aop/1571731439


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