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SUMMARY:Stephen Muirhead (The University of Melbourne)
DTSTART:20200924T070000Z
DTEND:20200924T080000Z
DTSTAMP:20260423T021406Z
UID:PVSeminar/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PVSeminar/2/
 ">The phase transition for planar Gaussian percolation models without posi
 tive associations</a>\nby Stephen Muirhead (The University of Melbourne) a
 s part of Probability Victoria Seminar (PVSeminar)\n\n\nAbstract\nGiven a 
 smooth stationary centred Gaussian field f on the plane and a level  ℓ  
 in  ℝ\, we study the connectivity properties of the set {f < ℓ}. We pr
 ove that the critical level is ℓc = 0 under only symmetry and (very mild
 ) correlation-decay assumptions\, which includes the important example of 
 the random plane wave. Since these models are not necessarily positively a
 ssociated (i.e. they do not enjoy the “Fortuin-Kasteleyn-Ginibre (FKG) i
 nequality”)\, many classical arguments from percolation/statistical mech
 anics do not apply\, and so these are a rare example of non-FKG models who
 se critical point can be rigorously computed.\n\nAlthough many arguments a
 re specific to the Gaussian setting we hope that our techniques may be ada
 pted to analyse other non-FKG models\, of which there are many important e
 xamples (e.g. anti-ferromagnetic Ising models\, certain regimes of the FK 
 model and O(n) loop models\, random current models\, Boolean models on non
 -Poisson point processes etc). This is joint work with Hugo Vanneuville an
 d Alejandro Rivera and will appear on arXiv very soon.\n
LOCATION:https://researchseminars.org/talk/PVSeminar/2/
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