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CATEGORIES:Combinatorics and Probability Seminar
SUMMARY:Extremal stationary values for random digraphs - G
uillem Perarnau (Polytechnic University of Catalon
ia)
DTSTART:20201119T160000Z
DTEND:20201119T170000Z
UID:TALK4339AT
URL:/talk/index/4339
DESCRIPTION:In this talk\, we will discuss the minimum positiv
e value of the stationary distribution of a random
walk on a directed random graph with given degree
s. While for undirected graphs the stationary dist
ribution is simply determined by the degrees\, the
graph geometry plays a major role in the directed
case. Understanding typical stationary values is
key to determining the mixing time of the walk\, a
s shown by Bordenave\, Caputo\, and Salez. However
\, typical results provide no information on the m
inimum value\, which is important for many applica
tions. Recently\, Caputo and Quattropani showed th
at the stationary distribution exhibits logarithmi
c fluctuations provided that the minimum degree is
at least 2. In this talk\, we show that dropping
the minimum degree condition may yield polynomiall
y smaller stationary values of the form n^{-(1+C+o
(1))}\, for a constant C determined by the degree
distribution. In particular\, C is the combination
of two factors: (1) the contribution of atypicall
y thin in-neighborhoods\, controlled by subcritica
l branching processes\; and (2) the contribution o
f atypically "light" trajectories\, controlled by
large deviation rate functions. As a by-product of
our proof\, we also determine the hitting and cov
er time in random digraphs. This is joint work wit
h Xing Shi Cai.\n_________________________________
_________________________\n\nMeeting ID: 830 2268
5017\nPasscode: 101833
LOCATION:https://bham-ac-uk.zoom.us/j/83022685017?pwd=L1RQc
lI2dmIvL2RXeUNCblpuanlBUT09
CONTACT:
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