Quasi-symétries des processus déterminantaux

Alexander Bufetov
I2M, Aix-Marseille Université
/user/alexander.bufetov/

Date(s) : 03/10/2014   iCal
11 h 00 min - 12 h 00 min

Quasi-symmetries of determinantal processes

The main result of this talk is that determinantal point processes on the real line corresponding to projection operators with integrable kernels are quasi-invariant, in the continuous case, under the group of diffeomorphisms with compact support (Theorem 1.4); in the discrete case, under the group of all finite permutations of the phase space (Theorem 1.6). The Radon-Nikodym derivative is computed explicitly and is given by a regularized multiplicative functional. Theorem 1.4 applies, in particular, to the sine-process, as well as to determinantal point processes with the Bessel and the Airy kernels; Theorem 1.6 to the discrete sine-process and the Gamma kernel process. The paper answers a question of Grigori Olshanski.

https://arxiv.org/abs/1409.2068

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