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SUMMARY:Asymptotic Expansions for a Class of Fredholm Pfaffians and Intera
 cting Particle Systems
DTSTART:20260605T120000Z
DTEND:20260605T133000Z
DTSTAMP:20260615T185500Z
UID:indico-event-16599@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Oleg Zaboronski (University of Warwick)\n\nSéminair
 e d'Analyse\nMotivated by the phenomenon of duality for interacting partic
 le systems we introduce two classes of Pfaffian kernels describing a numbe
 r of Pfaffian point processes in the "bulk" and at the "edge". Using the p
 robabilistic method due to Mark Kac\, we prove two  Szegő-type asymptoti
 c expansion theorems for the corresponding Fredholm Pfaffians. The idea of
  the proof is to introduce an effective random walk with transition densit
 y determined by the Pfaffian kernel\, express the logarithm of the Fredhol
 m Pfaffian through expectations with respect to the random walk\, and ana
 lyse the expectations using general results on random walks. We demonstrat
 e the utility of the theorems by calculating asymptotics for the empty int
 erval and non-crossing probabilities for a number of examples of Pfaffian 
 point processes: coalescing/annihilating Brownian motions\, massive coales
 cing Brownian motions\, real zeros of Gaussian power series and Kac polyno
 mials\, and real eigenvalues for the real Ginibre ensemble. (Joint work w
 ith Will FitzGerald and Roger Tribe.)\n \n========\nPour être informé d
 es prochains séminaires vous pouvez vous abonner à la liste de diffusion
  en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: "subs
 cribe seminaire_mathematique PRENOM NOM"(indiquez vos propres prénom et n
 om) et laissez le corps du message vide.\n\nhttps://indico.math.cnrs.fr/ev
 ent/16599/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/16599/
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