Marek Bozejko (Wroclaw)

On free infinite divisibility for classical Meixner distributions and generalized Gaussian Processes

vendredi 28 mars 2014, 9h30 - 10h30

Salle de réunion, espace Turing

In the first part of the talk we give idea why the symmetric Meixner
distribution,whose density are proportional to |\Gamma(t+ix)|^{2} are
freely infinitely divisible for t in interval (0,1/2] . The case t=1/2
corresponds to the law of Levy ‘s stochastic area, whose probability
density is 1/cosh(pi x).
In the second part we give connections of our problems on the free
probability and random matrix with generalized Gaussian process which we
started with Roland Speicher.

Main references:
1.S.Belinschi,M.Bozejko,F.Lehner,R.Specher, The normal distribution is free
infinitely divisible,Advances in Math. 226(2011),3677-3698.
2.M.Bozejko,T.Hasebe, On free infinitel divisibility for classical Meixner
distributions,Prob. Math Statistics, 33(2),2013,363-375 (also on arXiv).
3.M.Bozejko, W.Bozejko, Generalized Gaussian processes and relations with
random matrices and positive definite functions on permutation groups,
arXiv 2013.
4.M.Bozejko,R.Speicher, Interpolations between bosonic and fermionic
relations given by Brownian motions,Math.Z. 222(1996),135-160.