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SUMMARY:Michael Aizenman (Princeton)
DTSTART:20201210T160000Z
DTEND:20201210T173000Z
DTSTAMP:20260423T052709Z
UID:AQFP/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AQFP/3/">Mar
 ginal triviality of the scaling limits of 4D critical Ising and $\\Phi^4$ 
 models</a>\nby Michael Aizenman (Princeton) as part of Analysis\, Quantum 
 Fields\, and Probability\n\n\nAbstract\nThe talk will present the recent p
 roof that in four\ndimensions the spin fluctuations of Ising-type models a
 t their critical\npoints are Gaussian in their scaling limits (infinite vo
 lume\, vanishing\nlattice spacing).  Similar statement is proven for the s
 caling limits of\nmore general $\\Phi^4$ fields constructed through a latt
 ice cutoff. The\nproofs are facilitated by the systems’ random current r
 epresentation\, in\nwhich the deviation from Wick's law are expressed in t
 erms of\nintersection probabilities of random currents with prescribed sou
 rces.\nThis approach previously yielded such statements for D>4. Their rec
 ent\nextension to the marginal dimension was enabled by a multiscale analy
 sis\nof the critical clusters’ intersections.   (Joint work with Hugo\nD
 uminil-Copin.)\n
LOCATION:https://researchseminars.org/talk/AQFP/3/
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