The Evolution of the Mixing Rate
| dc.creator | Fountoulakis, Nikolaos | |
| dc.creator | Reed, Bruce | |
| dc.date | 2007-01-17 | |
| dc.date.accessioned | 2026-07-07T07:41:31Z | |
| dc.date.available | 2026-07-07T07:41:31Z | |
| dc.description | In this paper we present a study of the mixing time of a random walk on the largest component of a supercritical random graph, also known as the giant component. We identify local obstructions that slow down the random walk, when the average degree d is at most (ln n lnln n)^{1/2}, proving that the mixing time in this case is O((ln n/d)^2) asymptotically almost surely. As the average degree grows these become negligible and it is the diameter of the largest component that takes over, yielding mixing time O(ln n/ln d). We proved these results during the 2003-04 academic year. Similar results but for constant d were later proved independently by I. Benjamini, G. Kozma and N. Wormald. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701474 | |
| dc.identifier | http://arxiv.org/abs/math/0701474 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122137 | |
| dc.subject | Combinatorics | |
| dc.subject | Probability | |
| dc.subject | 05C80 (Primary), 60J10 (Secondary) | |
| dc.title | The Evolution of the Mixing Rate | |
| dc.type | text |