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CATEGORIES:Combinatorics and Probability Seminar
SUMMARY:Percolation in High-Dimensional Product Graphs - J
oshua Erde\, Graz
DTSTART:20221020T140000Z
DTEND:20221020T150000Z
UID:TALK5008AT
URL:/talk/index/5008
DESCRIPTION:A classic result of Erdős and Rényi describes the
phase transition that the component structure of t
he binomial random graph G(n\,p) undergoes when p
is around 1/n. Below this point\, the graph typica
lly contains only small components\, of logarithmi
c order\, whereas above this point many of these c
omponent coalesce to a unique `giant' component of
linear order\, and all other components are of lo
garithmic order. It has been observed that quantit
atively similar phase transitions occur in many ot
her percolation models\, and\, in particular\, wor
k of Ajtai\, Komlós and Szemerédi and of Bollobás\
, Kohayakawa and Łuczak shows that such a phenomen
a occurs in the percolated hypercube. We consider
this phase transition in percolation on graphs ari
sing from the cartesian product of many graphs and
show that\, under some mild conditions on the fac
tor graphs\, this phenomena is universal.\n\nJoint
with Sahar Diskin\, Mihyun Kang and Michael Krive
levich
LOCATION:LTC
CONTACT:Johannes Carmesin
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