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CATEGORIES:Probability
SUMMARY:Sharpness of the phase transition for level set pe
 rcolation of long-range correlated Gaussian fields
  - Stephen Muirhead (Melbourne)
DTSTART;TZID=Europe/London:20220222T140000
DTEND;TZID=Europe/London:20220222T150000
UID:TALK170636AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/170636
DESCRIPTION:We study the phase transition in the connectivity 
 of the excursion sets of long-range correlated Gau
 ssian fields. Our main result establishes `sharpne
 ss' of the transition for a wide class of fields\,
  discrete and continuous\, whose correlations deca
 y algebraically with exponent \\alpha \\in (0\,d)\
 , including the Gaussian free field on Z^d\, d \\g
 e 3 (\\alpha = d-2)\, the Gaussian membrane model 
 on Z^d\, d \\ge 5 (\\alpha = d - 4)\, among other 
 examples. This result is new for all models in dim
 ension d \\ge 3 except the Gaussian free field\, f
 or which sharpness was proven in a recent breakthr
 ough by Duminil-Copin\, Goswami\, Rodriguez and Se
 vero\; even then\, our proof is simpler and yields
  new near-critical information on the percolation 
 density.
LOCATION:MR12
CONTACT:Perla Sousi
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