Rates of Convergence for the Planar Discrete Green's Function in Pacman\n Domains

2020/05/09 by Christian Beneš, Benes, Christian
Computer Science · Mathematics · #31A15 (Secondary) #60G50 (Primary) #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2005.04514

openalex publication_date 2020/05/09 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We obtain upper bounds for the rates of convergence for the simple random\nwalk Green's function in the domains D_\α =\nD_\α(n)= re^i\θ\∈ \ℂ:0 <\θ<2\π-\α,\n0<r<2n -z₀, where z₀\∈\ℤ² is a point closest to\nne^i(\π-\α/2). The rate depends on the angle of the wedge and is what\nwas suggested by the sharpest available results in the extreme cases \α\n=0 and \α=\π. Our proof uses the KMT coupling between random walk and\nBrownian motion.\n

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