The Difference Between a Discrete and Continuous Harmonic Measure
dc.contributor.author | Jiang, Jianping | |
dc.contributor.author | Kennedy, Tom | |
dc.date.accessioned | 2018-05-30T22:07:36Z | |
dc.date.available | 2018-05-30T22:07:36Z | |
dc.date.issued | 2017-12 | |
dc.identifier.citation | Jiang, J. & Kennedy, T. J Theor Probab (2017) 30: 1424. https://doi.org/10.1007/s10959-016-0695-3 | en_US |
dc.identifier.issn | 0894-9840 | |
dc.identifier.issn | 1572-9230 | |
dc.identifier.doi | 10.1007/s10959-016-0695-3 | |
dc.identifier.uri | http://hdl.handle.net/10150/627847 | |
dc.description.abstract | We consider a discrete-time, continuous-state random walk with steps uniformly distributed in a disk of radius h. For a simply connected domain D in the plane, let omega(h)(0, .; D) be the discrete harmonic measure at 0 is an element of D associated with this random walk, and omega(0, .; D) be the (continuous) harmonic measure at 0. For domains D with analytic boundary, we prove there is a bounded continuous function sigma(D)(z) on partial derivative D such that for functions g which are in C2+sigma (partial derivative D) for some alpha > 0 we have lim(h down arrow 0) integral(partial derivative D) g(xi)omega(h)( 0, vertical bar d xi vertical bar; D) - integral(partial derivative D) g(xi)omega(0, vertical bar d xi vertical bar; D)/h = integral(partial derivative D) g(z)sigma(D)(z)vertical bar dz vertical bar. We give an explicit formula for sigma(D) in terms of the conformal map from D to the unit disk. The proof relies on some fine approximations of the potential kernel and Green's function of the random walk by their continuous counterparts, which may be of independent interest. | en_US |
dc.description.sponsorship | NSF [DMS-1500850] | en_US |
dc.language.iso | en | en_US |
dc.publisher | SPRINGER/PLENUM PUBLISHERS | en_US |
dc.relation.url | http://link.springer.com/10.1007/s10959-016-0695-3 | en_US |
dc.rights | © Springer Science+Business Media New York 2016. | en_US |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject | Random walk | en_US |
dc.subject | Brownian motion | en_US |
dc.subject | Harmonic measure | en_US |
dc.subject | Dirichlet problem | en_US |
dc.title | The Difference Between a Discrete and Continuous Harmonic Measure | en_US |
dc.type | Article | en_US |
dc.contributor.department | Univ Arizona, Dept Math | en_US |
dc.identifier.journal | JOURNAL OF THEORETICAL PROBABILITY | en_US |
dc.description.note | 12 month embargo; published online: 07 June 2016 | en_US |
dc.description.collectioninformation | This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu. | en_US |
dc.eprint.version | Final accepted manuscript | en_US |
dc.source.journaltitle | Journal of Theoretical Probability | |
dc.source.volume | 30 | |
dc.source.issue | 4 | |
dc.source.beginpage | 1424 | |
dc.source.endpage | 1444 | |
refterms.dateFOA | 2017-06-07T00:00:00Z |