| Título: | Explicit Expanders with Cutoff Phenomena |
| Autores: |
Lubetzky, Eyal; Microsoft Research Sly, Allan; Microsoft Research |
| Fecha: | 2011-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Cutoff phenomenon; Random walks; Expander graphs; Explicit constructions 60B10, 60J10, 60G50, 05C81 |
| Descripción: | The cutoff phenomenon describes a sharp transition in the convergence of an ergodic finite Markov chain to equilibrium. Of particular interest is understanding this convergence for the simple random walk on a bounded-degree expander graph. The first example of a family of bounded-degree graphs where the random walk exhibits cutoff in total-variation was provided only very recently, when the authors showed this for a typical random regular graph. However, no example was known for an explicit (deterministic) family of expanders with this phenomenon. Here we construct a family of cubic expanders where the random walk from a worst case initial position exhibits total-variation cutoff. Variants of this construction give cubic expanders without cutoff, as well as cubic graphs with cutoff at any prescribed time-point. |
| Idioma: | No aplica |
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