@article{d69e9175dce84c84bc82209eb1593791,
title = "The rate of convergence of the Walk on Spheres Algorithm",
abstract = "In this paper we examine the rate of convergence of one of the standard algorithms for emulating exit probabilities of Brownian motion, the Walk on Spheres (WoS) algorithm. We obtain a complete characterization of the rate of convergence of WoS in terms of the local geometry of a domain.",
keywords = "Walk on spheres algorithm, harmonic measure, potential theory",
author = "Ilia Binder and Mark Braverman",
note = "Funding Information: Keywords and phrases: Walk on spheres algorithm, harmonic measure, potential theory Mathematics Subject Classification (2000): 60G42, 65C05, 31B25, 31B05 I. Binder and M. Braverman were partially supported by their respective NSERC Discovery grant. This research was partially conducted during the period the second author was employed by the Clay Mathematics Institute as a Liftoff Fellow, as a postdoctoral researcher with Microsoft Research New England, and as a faculty member at the University of Toronto. A preliminary version of this work appeared in the proceedings of the 20th ACM-SIAM Symposium on Discrete Algorithms (SODA09).",
year = "2012",
month = sep,
doi = "10.1007/s00039-012-0161-z",
language = "English (US)",
volume = "22",
pages = "558--587",
journal = "Geometric and Functional Analysis",
issn = "1016-443X",
publisher = "Birkhauser Verlag Basel",
number = "3",
}