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DTSTAMP:20260405T190808Z
UID:66d57d1857b75775530853@ist.ac.at
DTSTART:20241021T170000
DTEND:20241021T180000
DESCRIPTION:Speaker: Misha Basok\nhosted by Laszlo Erdös\, Jan Maas\nAbstr
 act: In 2013 Miller\, Watson and Wilson introduced the notion of a nesting
  field associated with a conformal loop ensemble (CLE). The nesting field 
 is supposed to count the number of CLE loops surrounding a given point min
 us its expectation\; to define this field rigorously\, they proved that th
 e number of CLE loops surrounding a disc of radius epsilon minus its expec
 tation\, considered as a function of the center of the disc\, converges in
  the space of distributions as epsilon tends to zero\, and the limit is co
 nformally invariant. We consider a similar nesting field defined with resp
 ect to the double-dimer loop ensemble\, i.e. the loop ensemble that appear
 s when one superimposes two independent dimer configurations. As this loop
  ensemble is conjectured to converge to CLE(4) in the scaling limit\, one 
 can expect the corresponding behaviour of the nesting field. In this talk 
 I want to report on the following two results concerning the double-dimer 
 nesting field in the upper half-plane: Local behaviour: we prove that\, fo
 r any fixed point in the upper half-plane\, the number of double-dimer loo
 ps surrounding this point minus its expectation converges to a normal dist
 ribution if rescaled properly. Note that the same statement for CLE loops 
 follows easily from conformal invariance.Global behaviour: building on the
  results of Kenyon\, Dubedat and B-Chelkak we prove that double-dimer nest
 ing fields converge to the nesting field of CLE(4).Based on the joint work
  with Konstantin Izyurov (University of Helsinki).
LOCATION:Central Bldg / O1 / Mondi 2 (I01.O1.008)\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Misha Basok: Nesting of double-dimer loops and CLE(4)
URL:https://talks-calendar.ista.ac.at/events/5347
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