Random walks with badly approximable numbers
| dc.creator | Hensley, Doug | |
| dc.creator | Su, Francis Edward | |
| dc.date | 2001-02-27 | |
| dc.date.accessioned | 2026-07-07T04:40:23Z | |
| dc.date.available | 2026-07-07T04:40:23Z | |
| dc.description | Using 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.description | 7 pages; to appear in DIMACS volume "Unusual Applications of Number Theory"; related work at http://www.math.hmc.edu/~su/papers.html | |
| dc.identifier | https://arxiv.org/abs/math/0102206 | |
| dc.identifier | http://arxiv.org/abs/math/0102206 | |
| dc.identifier | DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 64 (2004), 95-101. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61009 | |
| dc.subject | Probability | |
| dc.subject | Number Theory | |
| dc.subject | 60B15 (Primary) 11J13, 11K38, 11K60 (Secondary) | |
| dc.title | Random walks with badly approximable numbers | |
| dc.type | text |