Discrepancy convergence for the drunkard's walk on the sphere

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dc.creatorSu, Francis Edward
dc.date2001-02-27
dc.date.accessioned2026-07-07T04:40:22Z
dc.date.available2026-07-07T04:40:22Z
dc.descriptionWe analyze the drunkard's walk on the unit sphere with step size theta and show that the walk converges in order constant/sin^2(theta) steps in the discrepancy metric. This is an application of techniques we develop for bounding the discrepancy of random walks on Gelfand pairs generated by bi-invariant measures. In such cases, Fourier analysis on the acting group admits tractable computations involving spherical functions. We advocate the use of discrepancy as a metric on probabilities for state spaces with isometric group actions.
dc.description20 pages; to appear in Electron. J. Probab.; related work at http://www.math.hmc.edu/~su/papers.html
dc.identifierhttps://arxiv.org/abs/math/0102205
dc.identifierhttp://arxiv.org/abs/math/0102205
dc.identifierElectronic Journal of Probability 6 (2001) no. 2, 1-20.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61008
dc.subjectProbability
dc.subjectRepresentation Theory
dc.subject60B15 (Primary) 43A85 (Secondary)
dc.titleDiscrepancy convergence for the drunkard's walk on the sphere
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