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SUMMARY:Sharpness of the phase transition for level set percolation of lon
 g-range correlated Gaussian fields - Stephen Muirhead (Melbourne)
DTSTART:20220222T140000Z
DTEND:20220222T150000Z
UID:TALK170636@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:We study the phase transition in the connectivity of the excur
 sion sets of long-range correlated Gaussian fields. Our main result establ
 ishes `sharpness' of the transition for a wide class of fields\, discrete 
 and continuous\, whose correlations decay algebraically with exponent \\al
 pha \\in (0\,d)\, including the Gaussian free field on Z^d\, d \\ge 3 (\\a
 lpha = 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 dimension
  d \\ge 3 except the Gaussian free field\, for which sharpness was proven 
 in a recent breakthrough by Duminil-Copin\, Goswami\, Rodriguez and Severo
 \; even then\, our proof is simpler and yields new near-critical informati
 on on the percolation density.
LOCATION:MR12
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