Card shuffling and diophantine approximation
| dc.creator | Angel, Omer | |
| dc.creator | Peres, Yuval | |
| dc.creator | Wilson, David B. | |
| dc.date | 2007-07-20 | |
| dc.date | 2008-06-17 | |
| dc.date.accessioned | 2026-07-07T09:44:36Z | |
| dc.date.available | 2026-07-07T09:44:36Z | |
| dc.description | The ``overlapping-cycles shuffle'' mixes a deck of $n$ cards by moving either the $n$th card or the $(n-k)$th card to the top of the deck, with probability half each. We determine the spectral gap for the location of a single card, which, as a function of $k$ and $n$, has surprising behavior. For example, suppose $k$ is the closest integer to $αn$ for a fixed real $α\in(0,1)$. Then for rational $α$ the spectral gap is $Θ(n^{-2})$, while for poorly approximable irrational numbers $α$, such as the reciprocal of the golden ratio, the spectral gap is $Θ(n^{-3/2})$. | |
| dc.description | Published in at http://dx.doi.org/10.1214/07-AAP484 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0707.2994 | |
| dc.identifier | http://arxiv.org/abs/0707.2994 | |
| dc.identifier | Annals of Applied Probability 2008, Vol. 18, No. 3, 1215-1231 | |
| dc.identifier | doi:10.1214/07-AAP484 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162931 | |
| dc.subject | Probability | |
| dc.subject | 60J10 (Primary) 60C05 (Secondary) | |
| dc.title | Card shuffling and diophantine approximation | |
| dc.type | text |