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DTSTAMP:20211206T055418Z
UID:1638291300@ist.ac.at
DTSTART:20211130T175500
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DESCRIPTION:Speaker: Marcin Lis\nhosted by M. Beiglböck\, N. Berestycki\,
L. Erdös\, J. Maas\, F. Toninelli\nAbstract: The double random current (D
RC) model is a natural percolation model whose geometric properties are in
timately related to spin correlations of the Ising model. In two dimension
s\, it moreover carries an integer valued height function on the graph\, c
alled the nesting field. We study the critical DRC model on bounded domain
s of the square lattice. We fully describe the joint scaling limit of the
(primal and dual) DRC clusters and the nesting field as the lattice mesh s
ize vanishes. We prove that the nesting field becomes the Dirichlet Gaussi
an free field (GFF) in this limit\, and that the outer boundaries of the D
RC clusters with free boundary conditions are the conformal loop ensemble
with $\\kappa=4$ (CLE4) coupled to that GFF. Moreover\, we also show that
the inner boundaries of the DRC clusters form a two-valued local set with
values ${\\mp 2\\lambda\, (2\\sqrt2 \\mp 2) \\lambda}$ for the field restr
icted to a CLE4 loop with boundary value $\\pm 2\\lambda$. Our proof is a
combination of exact solvability of the Ising model\, new crossing estimat
es for the DRC model (which does not possess the FKG property)\, and a car
eful analysis of the structure of two-valued local sets of the continuum G
FF. This is joint work with Hugo Duminil-Copin and Wei Qian.
LOCATION:Online via Zoom\, IST Austria
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Marcin Lis: Conformal invariance of critical double random currents
URL:https://talks-calendar.app.ist.ac.at/events/3410
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