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SUMMARY:On free energy in non-convex mean-field spin glass models
DTSTART:20250603T075000Z
DTEND:20250603T085000Z
DTSTAMP:20260504T062300Z
UID:indico-event-14328@indico.math.cnrs.fr
DESCRIPTION:Speakers: Hong-Bin Chen (IHES)\n\nWe start by reviewing the cl
 assical Sherrington-Kirkpatrick (SK) model. In this model\, +1/-1-valued s
 pins interact with each other subject to random coupling constants. The co
 variance of the random interaction is quadratic in terms of spin overlaps.
  Parisi proposed the celebrated variational formula for the limit of free 
 energy of the SK model in the 80s\, which was later rigorously verified in
  the works by Guerra and Talagrand. This formula has been generalized in v
 arious settings\, for instance\, to vector-valued spins\, by Panchenko. Ho
 wever\, in these cases\, the convexity of the interaction is crucial. In g
 eneral\, the limit of free energy in non-convex models is not known and we
  do not have variational formulas as valid candidates. Here\, we report re
 cent progress through the lens of the Hamilton-Jacobi equation. Under the 
 assumption that the limit of free energy exists\, we show that the value o
 f the limit is prescribed by a characteristic line\; and the limit (as a f
 unction) satisfies an infinite-dimensional Hamilton-Jacobi equation "almos
 t everywhere". This talk is based on a joint work with Jean-Christophe Mou
 rrat.\n\nhttps://indico.math.cnrs.fr/event/14328/
LOCATION:Salle F. Pellos (1R2-207)
URL:https://indico.math.cnrs.fr/event/14328/
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