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2021 Rates of convergence for the planar discrete Green’s function in Pacman domains
Christian Beneš
Author Affiliations +
Electron. J. Probab. 26: 1-14 (2021). DOI: 10.1214/21-EJP599

Abstract

We obtain upper bounds for the rates of convergence for the simple random walk Green’s function in the domains Dα=Dα(n)={rei𝜃C:0<𝜃<2πα,0<r<2n}z0, where z0Z2 is a point closest to nei(πα2). The rate depends on the angle of the wedge and is what was suggested by the sharpest available results in the extreme cases α=0 and α=π. Our proof uses the KMT coupling between random walk and Brownian motion.

Funding Statement

The author gratefully acknowledges support through PSC-CUNY Award # 61514-00 49.

Acknowledgments

The author wishes to thank the referee for carefully reading the paper and for suggesting some improvements.

Citation

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Christian Beneš. "Rates of convergence for the planar discrete Green’s function in Pacman domains." Electron. J. Probab. 26 1 - 14, 2021. https://doi.org/10.1214/21-EJP599

Information

Received: 28 September 2020; Accepted: 3 March 2021; Published: 2021
First available in Project Euclid: 7 April 2021

arXiv: 2005.04514
Digital Object Identifier: 10.1214/21-EJP599

Subjects:
Primary: 31A15, 60G50

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