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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.\n\
nThe question of parameter continuity with respect to local weak convergenc
e arises also for infinite graphs. We examine Schramm's conjectures about t
he locality of percolation critical probability in the class of unimodular
random graphs, which is a common generalization of invariant subgraphs of C
ayley graphs and local weak limits of random graphs. We extend the definiti
ons of critical probabilities to this class and investigate the relationshi
p between the different notions of criticality. We give conditions that imp
ly the convergence of the percolation critical probability along local weak
convergent sequences, and we show by examples that the locality conjecture
does not hold in the generality of unimodular random graphs. The results a
re joint work with Gábor Pete and Ádám Timár.\n\nThe talk is the internal d
efence of the PhD thesis.
DTSTAMP:20210117T065609Z
DTSTART;TZID=Europe/Budapest:20190708T140000
DTEND;TZID=Europe/Budapest:20190708T160000
SEQUENCE:1
TRANSP:OPAQUE
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