A finite ergodic Markov chain exhibits cutoff if its distance to equilibrium remains close to its initial value over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Originally discovered in the context of card shuffling (Aldous and Diaconis in Am Math Mon 93:333–348, 1986), this remarkable phenomenon is now rigorously established for many reversible chains. Here we consider the non-reversible case of random walks on sparse directed graphs, for which even the equilibrium measure is far from being understood. We work under the configuration model, allowing both the in-degrees and the out-degrees to be freely specified. We establish the cutoff phenomenon, determine its precise window and prove that the cutoff profile approaches a universal shape. We also provide a detailed description of the equilibrium measure.
|Titolo:||Random walk on sparse random digraphs|
CAPUTO, PIETRO (Corresponding)
|Data di pubblicazione:||2018|
|Citazione:||Random walk on sparse random digraphs / Bordenave, Charles; Caputo, Pietro; Salez, Justin. - In: PROBABILITY THEORY AND RELATED FIELDS. - ISSN 0178-8051. - 170:3-4(2018), pp. 933-960.|
|Appare nelle tipologie:||1.1 Articolo in rivista|