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UID:35328dusrordemi5bpq3un56b0@google.com
CATEGORIES:{lang hu}Sztochasztika szeminárium{/lang}{lang en}Stochastics seminar{/lang}
SUMMARY:Beringer Dorottya (Rényi Intézet): Local weak limits of random graphs and parameter continuity
LOCATION:Szeged, Aradi vértanúk tere 1., Szőkefalvi terem.
DESCRIPTION;ENCODING=QUOTED-PRINTABLE:Abstract. The theory of local weak convergence provides a useful tool to st
udy parameters of large finite graphs that are determined by the local stru
cture of the graph. The observations of Liu, Slotine and Barabási (2011) su
ggested that the matching ratio of directed graphs, which is closely relate
d to an important parameter in control theory, is in some cases essentially
determined by the degrees of the graphs and converges along local weak con
vergent sequences. We give the precise formulation and rigorous proofs of t
hese statements about the concentration and limiting properties of the matc
hing ratio of random graphs. The results are joint work with Ádám Timár.

The question of parameter continuity with respect to local weak conv
ergence arises also for infinite graphs. We examine Schramm's conjectures a
bout the locality of percolation critical probability in the class of unimo
dular random graphs, which is a common generalization of invariant subgraph
s of Cayley graphs and local weak limits of random graphs. We extend the de
finitions of critical probabilities to this class and investigate the relat
ionship between the different notions of criticality. We give conditions th
at imply the convergence of the percolation critical probability along loca
l weak convergent sequences, and we show by examples that the locality conj
ecture does not hold in the generality of unimodular random graphs. The res
ults are joint work with Gábor Pete and Ádám Timár.

The talk is th
e internal defence of the PhD thesis.
DTSTAMP:20201130T130118Z
DTSTART;TZID=Europe/Budapest:20190708T140000
DTEND;TZID=Europe/Budapest:20190708T160000
SEQUENCE:1
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