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CATEGORIES:Probability
SUMMARY:Percolation\, long-range correlations and critical
exponents on transient graphs - Alexander Drewitz
(Universität zu Köln)
DTSTART;TZID=Europe/London:20220524T140000
DTEND;TZID=Europe/London:20220524T150000
UID:TALK174956AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/174956
DESCRIPTION:Percolation models have been playing a fundamental
role in statistical physics for several decades b
y now. They had initially been investigated in the
gelation of polymers during the 1940s by chemistr
y Nobel laureate Flory and Stockmayer. From a math
ematical point of view\, the birth of percolation
theory was the introduction of Bernoulli percolati
on by Broadbent and Hammersley in 1957\, motivated
by research on gas masks for coal miners. One of
the key features of this model is the inherent sto
chastic independence which simplifies its investig
ation\, and which has lead to deep mathematical re
sults. During recent years\, the investigation of
the more realistic and at the same time more compl
ex situation of percolation models with long-range
correlations has attracted significant attention.
\n\nWe will exhibit some recent progress for the G
aussian free field with a particular focus on the
understanding of the critical parameters in the as
sociated percolation models. What is more\, we als
o survey recent progress in the understanding of t
he model at criticality via its critical exponents
as well as the universality in the local geometry
of the underlying graph.\n\nThis talk is based on
joint works with A. Prevost (U Cambridge) and P.-
F. Rodriguez (Imperial College).
LOCATION:MR12\, Centre for Mathematical Sciences
CONTACT:Perla Sousi
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