Dipartimento di Matematica, Sapienza Università di Roma         

        

Martedì 29 novembre

Ore 14:00, Aula di Consiglio

Seminario di Probabilità e Statistica Matematica

 

 

Pietro Caputo, Dipartimento di Matematica, Università di Roma Tre

 

Titolo: Random walk on sparse random directed graphs

 

Abstract: A random walk on a finite graph exhibits cutoff if its distance from stationarity remains close to the initial value for a certain number of iterations and then abruptly drops to near zero on a much shorter time scale. Originally discovered in the context of card shuffling by Aldous and Diaconis in 1986, this remarkable phenomenon is now rigorously established for many reversible chains. Here we consider the non-reversible case of random walks on sparse random directed graphs, for which even the stationary distribution is far from being understood. We establish the cutoff phenomenon, determine its time window and prove that the cutoff profile approaches a universal gaussian shape. Moreover, we determine an explicit recursive equation characterizing the stationary distribution. This talk is based on joint work with Charles Bordenave and Justin Salez.

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