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
- 24.04.2012 Piotr Sniady
Trajectiories of jeu-de-taquin and semicircular law
In an infinite Young tableau we remove the corner box. In this way an avalanche of sliding boxes is
created. Asymptotic behavior of this avalanche is closely related to Robinson-Schensted-Knuth (RSK)
correspondence and the representation theory of the infinite symmetric group. Wigner's semicircular law
plays an important role.
This is a joint work with Dam Romik.
- 02.05.2012 Tobias Mai and Soren Moller
On Wigner chaos and the fourth moment
condition
- 06.06.2012 Octavio Arizmendi Echegaray
Convergence of the fourth moment for infinitely divisible distributions
In a seminal paper, Nualart and Peccati (2005),proved that for multiple Wiener integrals with variance 1
in a fixed chaos, the convergence of the 4th moment to 3 implies the convergence in law to the Gaussian
distribution. Later, Kemp, Nourdin, Peccati and Speicher (2011) proved the analogous theorem in
free probability.
In this talk we will explain a similar result for both classically and freely infinitely divisible
measures. Namely, when restricted to classically (resp freely) infinitely divisible distribution, the
convergence of the first four moments to the Gaussian (resp. Semicircle distribution) implies the
convergence in law.
- 13.06.2012 Michael Anshelevich
Generators of some non-commutative stochastic processes: proofs and further results
The following results are well known. A Levy process is a Markov process. Its transition operators form
a semigroup of contractions. The generator of this semigroup can be written down explicitly using
Fourier analysis.
I will discuss the same questions in the framework of free Levy processes (process with freely independent,
stationary increments). Some of the new difficulties in this case are (1) there is no free Fourier
transform, and (2) the transition operators no longer form a semigroup. Nevertheless, most of the results
from the first paragraph carry over, with the generators written down explicitly as singular integral
operators.
- 12.07.2012 John Williams
The inclusion of monotone convolution in the Bercovici-Pata
bijection
I will discuss recent work in which the bijection of infinitely divisible measures and triangular arrays
in the various probability theories is extended to monotone convolution. The key to proving this theorem
is to treat F-transforms as composition operators and study these phenomenon using tools from semi-group
theory. In particular, we utilize the famous product formula due to Chernoff. We also prove a limited
converse to Chernoff's theorem for composition operators on certain spaces of analytic functions.
Aktualisiert am: 13. Juni 2012 Octavio Arizmendi
