On the Chung-Diaconis-Graham random process
| dc.creator | Hildebrand, Martin | |
| dc.date | 2005-08-23 | |
| dc.date | 2007-08-20 | |
| dc.date.accessioned | 2026-07-07T08:24:10Z | |
| dc.date.available | 2026-07-07T08:24:10Z | |
| dc.description | Chung, Diaconis, and Graham considered random processes of the form X_{n+1}=2X_n+b_n (mod p) where X_0=0, p is odd, and b_n for n=0,1,2,... are i.i.d. random variables on {-1,0,1}. If Pr(b_n=-1)= Pr(b_n=1)=βand Pr(b_n=0)=1-2β, they asked which value of βmakes X_n get close to uniformly distributed on the integers mod p the slowest. In this paper, we extend the results of Chung, Diaconis, and Graham in the case p=2^t-1 to show that for 0<β<=1/2, there is no such value of β. | |
| dc.description | 11 pages; This version corrects a flaw in the original version | |
| dc.identifier | https://arxiv.org/abs/math/0508427 | |
| dc.identifier | http://arxiv.org/abs/math/0508427 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136252 | |
| dc.subject | Probability | |
| dc.subject | 60B15 (Primary) 60J10 (Secondary) | |
| dc.title | On the Chung-Diaconis-Graham random process | |
| dc.type | text |