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UID:7875@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20160307T000000
DTEND;TZID=Europe/Paris:20160307T000000
DTSTAMP:20241120T205557Z
URL:https://www.i2m.univ-amu.fr/evenements/ergodic-theory-seminar-at-irmar
 -rennes/
SUMMARY: (...): Ergodic theory seminar at IRMAR (Rennes)
DESCRIPTION:: The classical De Finetti Theorem (1937) states that an exchan
 geable collection of random variables is a mixture of Bernoulli sequences.
  The first result of the talk is that determinantal point processes on Z i
 nduced by integrable kernels are quasi-invariant under the action of the i
 nfinite symmetric group. The Radon-Nikodym derivative is a regularized mul
 tiplicative functional on the space of configurations. A key example is th
 e discrete sine-process of Borodin\, Okounkov and Olshanski. The second re
 sult is a continuous counterpart of the first: namely\, it is proved that 
 determinantal point processes with integrable kernles on R\, a class that 
 includes processes arising in random matrix theory such as Dyson's sine-pr
 ocess\, or the processes with the Bessel kernel or the Airy kernel studied
  by Tracy and Widom\, are quasi-invariant under the action of the group of
  diffeomorphisms of the line with compact support. While no analogues of t
 hese results in higher dimensions are known\, in joint work with Yanqi Qiu
  it is shown that for determinantal point processes corresponding to Hilbe
 rt spaces of holomorphic functions on the complex plane C or on the unit d
 isk D\, the quasi-invariance under the action of the group of diffeomorphi
 sms with compact support also holds.\n\nLocation: Campus de Beaulieu\, bâ
 timents 22 et 23 - 263 avenue du Général Leclerc\, CS 74205 - 35042 Renn
 es Cedex - France
CATEGORIES:Event ERC IChaos
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