*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.*
*Tutti gli interessati sono invitati a partecipare.*
*Per qualsiasi richiesta di informazioni rivolgersi a
**piccioni(a)mat.uniroma1.it
<piccioni(a)mat.uniroma1.it>.*