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UID:7893@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20160219T180000
DTEND;TZID=Europe/Paris:20160219T193000
DTSTAMP:20241120T205600Z
URL:https://www.i2m.univ-amu.fr/evenements/quasi-symmetries-of-determinant
 al-point-processes/
SUMMARY:Alexander Bufetov (I2M\, CNRS\, Marseille): Quasi-Symmetries of Det
 erminantal Point Processes
DESCRIPTION:Alexander Bufetov: The first result of the talk is that determi
 nantal point processes on Z induced by integrable kernels are quasi-invari
 ant under the action of the infinite symmetric group. The Radon-Nikodym de
 rivative is a regularized multiplicative functional on the space of config
 urations. A key example is the discrete sine-process of Borodin\, Okounkov
  and Olshanski.\nThe second result is a continuous counterpart of the firs
 t: namely\, it is proved that determinantal point processes with integrabl
 e kernles on R\, a class that includes processes arising in random matrix 
 theory such as Dyson's sine-process\, or the processes with the Bessel ker
 nel or the Airy kernel studied by Tracy and Widom\, are quasi-invariant un
 der the action of the group of diffeomorphisms of the line with compact su
 pport.\nNo analogues of these results are known in higher dimensions. In j
 oint work with Yanqi Qiu it is shown\, however\, that for determinantal po
 int processes corresponding to Hilbert spaces of holomorphic functions on 
 the complex plane C or on the unit disk D\, the quasi-invariance under the
  action of the group of diffeomorphisms with compact support also holds.\n
 http://www.mathnet.ru/php/seminars.phtml?option_lang=rus&amp\;presentid=13
 443\nLocation: St. Petersburg Department of V.A. Steklov Institute of Math
 ematics of the Russian Academy of Sciences\, 27 Fontanka\, St. Petersburg\
 , Russia
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Alexander_Bufetov.jpg
CATEGORIES:Séminaire,Event ERC IChaos,Processus Déterminantaux (ERC
 IChaos)
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