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DTSTAMP:20260406T000406Z
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\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Marcin Lis: Conformal invariance of critical double random currents
URL:https://talks-calendar.ista.ac.at/events/3410
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