Random walks with badly approximable numbers

dc.creatorHensley, Doug
dc.creatorSu, Francis Edward
dc.date2001-02-27
dc.date.accessioned2026-07-07T04:40:23Z
dc.date.available2026-07-07T04:40:23Z
dc.descriptionUsing the discrepancy metric, we analyze the rate of convergence of a random walk on the circle generated by d rotations, and establish sharp rates that show that badly approximable d-tuples in R^d give rise to walks with the fastest convergence. We use the discrepancy metric because the walk does not converge in total variation. For badly approximable d-tuples, the discrepancy is bounded above and below by (constant)k^(-d/2), where k is the number of steps in the random walk. We show how the constants depend on the d-tuple.
dc.description7 pages; to appear in DIMACS volume "Unusual Applications of Number Theory"; related work at http://www.math.hmc.edu/~su/papers.html
dc.identifierhttps://arxiv.org/abs/math/0102206
dc.identifierhttp://arxiv.org/abs/math/0102206
dc.identifierDIMACS Ser. Discrete Math. Theoret. Comput. Sci. 64 (2004), 95-101.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61009
dc.subjectProbability
dc.subjectNumber Theory
dc.subject60B15 (Primary) 11J13, 11K38, 11K60 (Secondary)
dc.titleRandom walks with badly approximable numbers
dc.typetext

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