We obtain upper bounds for the rates of convergence for the simple random walk Green’s function in the domains , where is a point closest to . The rate depends on the angle of the wedge and is what was suggested by the sharpest available results in the extreme cases and . Our proof uses the KMT coupling between random walk and Brownian motion.
The author gratefully acknowledges support through PSC-CUNY Award # 61514-00 49.
The author wishes to thank the referee for carefully reading the paper and for suggesting some improvements.
"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