BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Guillem Perarnau (Universitat Politècnica de Catalunya) DTSTART:20200907T140000Z DTEND:20200907T150000Z DTSTAMP:20260423T052457Z UID:EPC/22 DESCRIPTION:Title: Ext remal stationary values for directed random graphs\nby Guillem Perarna u (Universitat Politècnica de Catalunya) as part of Extremal and probabil istic combinatorics webinar\n\n\nAbstract\n: In this talk\, we will discus s the minimum positive value of the stationary distribution of a random wa lk on a directed random graph with given (bounded) degrees. While for undi rected graphs the stationary distribution is simply determined by the degr ees\, the graph geometry plays a major role in the directed case. Understa nding typical stationary values is key to determining the mixing time of t he walk\, as shown by Bordenave\, Caputo\, and Salez. However\, typical re sults provide no information on the minimum value\, which is important for many applications. Recently\, Caputo and Quattropani showed that the stat ionary distribution exhibits logarithmic fluctuations provided that the mi nimum degree is at least 2. In this talk\, we show that dropping the minim um degree condition may yield polynomially smaller stationary values of th e form $n^{-(1+C+o(1))}$\, for a constant C determined by the degree distr ibution. In particular\, C is the combination of two factors: (1) the cont ribution of atypically thin in-neighborhoods\, controlled by subcritical b ranching processes\; and (2) the contribution of atypically "light" direct ed paths\, controlled by large deviation rate functions. As a by-product o f our proof\, we also determine the mean hitting time in random digraphs. This is joint work with Xing Shi Cai.\n LOCATION:https://researchseminars.org/talk/EPC/22/ END:VEVENT END:VCALENDAR