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DTSTART:20190331T030000
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BEGIN:VEVENT
DTSTAMP:20210515T012631Z
UID:1552404600@ist.ac.at
DTSTART:20190312T163000
DTEND:20190312T173000
DESCRIPTION:Speaker: Ioan Manolescu\nhosted by M. Beiglböck\, N. Berestyc
ki\, L. Erdös\, J. Maas\nAbstract: Uniform integer-valued Lipschitz funct
ions on a finite domain of the triangular lattice are shown to have variat
ions of logarithmic order in the radius of the domain.The level lines of s
uch functions form a loop O(2) model on the edges of the hexagonal lattice
with edge-weight one. An infinite-volume Gibbs measure for the loop O(2)
model is constructed as a thermodynamic limit and is shown to be unique. I
t contains only finite loops and has properties indicative of scale-invari
ance: macroscopic loops appearing at every scale. The existence of the inf
inite-volume measure carries over to height functions pinned at 0\; the un
iqueness of the Gibbs measure does not.The proof is based on a representat
ion of the loop O(2) model via a pair of spin configurations that are show
n to satisfy the FKG inequality. We prove RSW-type estimates for a certain
connectivity notion in the aforementioned spin model.Based on joint work
with Alexander Glazman.
LOCATION:Uni Wien\, HS 11\, 2. OG\, OMP 1\, IST Austria
ORGANIZER:caroline.petz@ist.ac.at
SUMMARY:Uniform Lipschitz functions on the triangular lattice have logarith
mic variations
URL:https://talks-calendar.app.ist.ac.at/events/1848
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