Prof. Dr. Roland Speicher
Octavio Arizmendi Echegaray
Oberseminar zur Freien Wahrscheinlichkeit
In diesem Seminar behandeln wir Themen aus der aktuellen Forschung zur Freien Wahrscheinlichkeit.
Zeit und Ort
mittwochs, 16-18 Uhr, SR5 (215)
Vorträge
- 23.10.2012 Octavio Arizmendi
Superconvergence in Non-Commutative Probability: A combinatorial approach.
In this the talk I will explain how to use cumulants to give a simple proof of an instance of the so-called
superconvergence of normalized sums of free random variables. Namely, that the operator norm of normalized
sums of bounded free random variables with mean 0 and variance1, converge to 2. Moreover, our approach
generalizes in a straightforward way to monotone and boolean independence and q-convoluion.
- 12.11.2012 Roland Friedrich
On certain Algebraic Structures in Free Probability Theory
In this talk we shall discuss some algebraic structures which are inherently related to free probability
theory, as we found. This permits us to give a web of correspondences between different but isomorphic
rings. In particular it extends the known boxed operations in free harmonic analysis, such that the set of
distributions becomes a commutative unital ring. This will be illustrated by examining some of the most
important distributions.
- 14.11.2012 Stephen Avsec
A characterization of exchangable noncommutative brownian motion
- Donnerstag, 17.1.2013, 16-18h, SR6 (216) Pierre Tarrago
Noncommutative Symmetric Functions
This talk aims to briefly introduce to a noncommutative generalization of
the Hopf algebra of the symmetric
functions. These algebra shows a lot of
similarities with the commutative one, going from algebraic to
representation properties. Time permitting I will also present a new kind
of generalization containing
the old one.
- Mittwoch, 20.2.2013, 16-18h, SR6 (216) Marek Bozejko
New Generalized Gaussian processes and free infinitely divisibility for classical Meixner distributions
Abstract: In my talk we will present the following subjects:
1. Generalized Gaussian processes related to the functions on pair-partition - the number of singletons
and others.
2.Connections with Markov random matrices as in the paper of Bryc,Dembo,Jiang.
3.Positive definite functions and normson permutation group.
4.Free infinitely divisibility of 1/cosh law and others symmetric Meixner distributions connected with
Meixner-Pollaczek polynomials.
5.Noncommutative Levy processes of anyonic type ; q-Gaussian for |q|=1 and related Hecke deformations.
References:
1.M.Bozejko , W.Bozejko, Generalized Gaussian processes and relations with random matrices and positive
definite functions on permutations groups, arXiv 2013.
2.M.Bozejko, E.Lytvynov, J.Wysoczanski, Noncommutative Levy Processes for Generalized(Particularly Anyon)
Statistics, Comm.Math.Phys. 313(2012) 535-569.
3.M.Bozejko, Deformed Fock spaces, Hecke operators and Monotone Fock space of Muraki, Demonstratio
Mathematica, XLV, 2012, 399-413
- Mittwoch, 27.2.2013, 16-18h, SR6 (216) Sören Möller (Odense, Denmark)
A law of large numbers for the free multiplicative convolution - distributions and observations
In classic probability the multiplicative law of large numbers follows from the additive as a corollary.
This is not the case in free probability, so although an additive law has been proved in [Lindsay-Pata, 1997]
the multiplicative law was only proved recently in [Tucci, 2010] for measures on the positive real line
with compact support. In 2012, in joint work with Uffe Haagerup, we gave a new proof of the result removing
the assumption of compact support. In this talk I will present the result and discuss distributions that
arise in this context and other observations related to the result.
Aktualisiert am: 18.2.2013 Tobias Mai