Discrete Harmonic Analysis and Noncommutative Probability

About the seminar

Seminar of the Mathematical Analysis Group in Institute of Mathematics, University of Wroclaw.

The main organizer: prof. Marek Bożejko

Time and place: every Thursday, 10.00 - 12.00 Institute of Mathematics, Wrocław University, room 604.

Topics: commutative and non-commutative harmonic analysis, quantum groups, combinatorics, quantum probability, free probability, Young diagrams, random matrices, convolutions of measures, ...

People you may meet here: Marek Bożejko (IMPAN), Biswarup Das, Wiktor Ejsmont (Uniwersytet Ekonomiczny), Rafał Kobuszewski, Anna Krystek (Politechnika Wrocławska), Romuald Lenczewski (Politechnika Wrocławska), Wojciech Młotkowski, Piotr Śniady, Anna Wysoczańska-Kula, Janusz Wysoczański

See also:

Current schedule:

Thursday, 19 October, 2017, 10:00-12:00, room 604

Maria Elena Griseta (University of Bari Aldo Moro)

Distributions on non-symmetric position operators on Weakly Monotone Fock Space

In this talk we investigate the distributions for sums of random variables $$x_i={a_i}^{-}+{a_i}^{†}+\lambda {a_i}^0,$$ where ${a_i}^{-}$, ${a_i}^{†}$ and ${a_i}^0$ denote respectively annihilation, creation and conservation operators on the Weakly Monotone Fock Space and $\lambda\in \mathbb{R}$. We start considering sum of position operators (case $\lambda=0$): after obtaining a recursive formula for the moments \[ \mu_{m,n} := \omega_{\Omega}\bigg(\bigg(\sum_{k=1}^{m}(A_{k}+A_{k}^{\dagger})\bigg)^{2n}\bigg) \] where $\Omega=1\oplus 0\oplus 0 \oplus 0\oplus \ldots$ is the vacuum vector and $\omega_{\Omega}(\cdot)=\left\langle \Omega,\cdot\Omega\right\rangle$ is the vacuum expectation, we calculate the Cauchy Transform of the distribution measure and the density for $m=2$. Finally we compute the distribution of a single random variable $x_i$ with respect to the vacuum state for the general case $\lambda\neq 0$.



Previous talks:

Thursday, 13 October, 2017, 10:00-12:00, room 604

Anna Wysoczańska-Kula

Związki teorii kohomologii z procesami Levy'ego na zwartych grupach kwantowych

W referacie opowiem o nieprzemiennych procesach Levy'ego definiowanych na grupach kwantowych i próbach ich klasyfikacji. Jedną z nich jest badanie istnienia rozkładu typu Levy'ego-Chinczyna. Okazuje się, że istnienie takiego rozkładu jest zagwarantowane przez pewne warunki kohomologiczne (choć nie jest im równoważne). Do zobrazowania opisanej teorii posłużą uniwersalne grupy kwantowe.


Thursday, 28 September, 2017 10:15-12:00, room 604

Wiktor Ejsmont

Cancellation phenomenon in free probability II

I am going to continue my previous discussion about the cancellation phenomenon of sample variance.



Past schedule for the year 2016/2017
Past schedule for the year 2015/2016
Past schedule for the year 2014/2015
Past schedule for the year 2013/2014
Past schedule for the year 2012/2013
Past schedule for the year 2011/2012
Past schedule for the year 2010/2011
Past schedule for the year 2009/2010
Past schedule for the year 2008/2009
Past schedule for the year 2007/2008
Past schedule for the year 2006/2007
Past schedule for the year 2005/2006
Past schedule for the year 2004/2005

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