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TZID:Europe/Paris
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UID:0-1045@lptms.universite-paris-saclay.fr
DTSTART;TZID=Europe/Paris:20250624T110000
DTEND;TZID=Europe/Paris:20250624T120000
DTSTAMP:20250619T151150Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/seminaire-du-lptm
 s-bertrand-lacroix-a-chez-toine-kcl-uk/
SUMMARY:Séminaire du LPTMS : Bertrand Lacroix a chez Toine (KCL\, UK) - Sa
 lle des séminaires du FAST et du LPTMS\, bâtiment Pascal n°530 - 24 Jui
 n 25 11:00
DESCRIPTION:Superposition of plane waves in high spatial dimensions: from l
 andscape complexity to the ground state value\n&nbsp\;\nBertrand Lacroix a
  chez Toine (KCL\, UK)\n&nbsp\;\n\nWe will discuss some statistical proper
 ties of a class of models of high-dimensional random landscapes defined in
  a Euclidean space of large dimension $N\\gg 1$ via a superposition of $M$
  plane waves whose amplitudes\, directions of the wavevectors\, and phases
  are taken to be random. Our main efforts are directed towards deriving\, 
 and then analysing for $N\\to \\infty\, M\\to \\infty$ while keeping $\\al
 pha=M/N$ finite\,\n(i)  the rates of asymptotic exponential growth with $
 N$ of the mean number of all critical points and of local minima known as 
 the annealed complexities and\n(ii)  the expression for the mean (also ex
 pected to be typical) value of the deepest landscape minimum (the ground-s
 tate energy).\nIn particular\, for the latter we derive the Parisi-like op
 timization functional and\nanalyze conditions for the optimizer to reflect
  various phases:  replica-symmetric\, one-step and full replica symmetry 
 broken\, as well as criteria for the continuous\,  Gardner and random fir
 st order transitions between those phases. This work is done in collabora
 tion with Yan V. Fyodorov (King’s College London).\n\nRef.: arXiv prepri
 nt arXiv:2411.09687\n
CATEGORIES:seminars
LOCATION:Salle des séminaires du FAST et du LPTMS\, bâtiment Pascal n°53
 0\, rue André Riviere\, Orsay\, 91405\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=rue André Riviere\, Orsay\
 , 91405\, France;X-APPLE-RADIUS=100;X-TITLE=Salle des séminaires du FAST 
 et du LPTMS\, bâtiment Pascal n°530:geo:0,0
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TZID:Europe/Paris
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DTSTART:20250330T030000
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