Discrete Harmonic Analysis and Noncommutative Probability

About the seminar

Seminar of the Research Group in Mathematical Analysis (Zakład Analizy Matematycznej) in Institute of Mathematics, University of Wroclaw.

The main organizer: prof. Marek Bożejko (IMPAN)

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), Adrian Dacko, Biswarup Das, Wiktor Ejsmont, Anna Krystek (Politechnika Wrocławska), Romuald Lenczewski (Politechnika Wrocławska), Wojciech Młotkowski, Lahcen Oussi, Anna Wysoczańska-Kula, Janusz Wysoczański

See also:

Current seminar schedule:

Tursday, 07. November 2019 - 10:15, room 602

Adrian Dacko

V-monotoniczne centralne twierdzenie graniczne

W referacie przypomnimy pojęcie V-monotonicznej niezależności, sformułujemy odpowiednie centralne twierdzenie graniczne oraz omówimy jego kombinatorykę. Zostanie przedstawione podejście do uzyskania rekurencji na momenty parzystego rzędu standardowego V-monotonicznego rozkładu gaussowskiego (przy pomocy odpowiednich operatorów gaussowskich określonych na tzw. ciągłej V-monotonicznej przestrzeni Focka). Z tej rekurencji, rozwiązując odpowiednie zagadnienie początkowe, na które składa się równanie różniczkowe zwyczajne typu Abela (II-go rodzaju), otrzymuje się funkcję tworzącą momenty tego rozkładu w postaci uwikłanej oraz, co za tym idzie, jego część absolutnie ciągłą (także w postaci uwikłanej).


Previous talks:

Tursday, 30. October 2019 - 10:15, room 602

Piotr M. Hajac (IMPAN)

V-monotoniczne centralne twierdzenie graniczneFrom pushouts to pullbacks: a sample of noncommutative topology

In topology, pushouts are formal recipes for collapsing and gluing topological spaces. For instance, shrinking the boundary circle of a disc to a point yields a sphere, shrinking the equator of a sphere to a point gives two spheres joined at the point, collapsing the boundary of a solid torus to a circle, or gluing two solid tori over their boundaries, produces a three-sphere. In noncommutative topology, such procedures are expressed in terms of pullbacks of C*-algebras. It turns out that one can visualize a pullback of C*-algebras of graphs as a pushout of these graphs thus providing much needed intuition to the abstract setting of operator algebras. The goal of this talk is to discuss how to make this visualization rigorous by conceptualizing abundant examples from noncommutative topology that lead to a new concept of morphisms of graphs. In particular, we replace the standard idea of mapping vertices to vertices and edges to edges by the more flexible idea of mapping finite paths to finite paths. (Based on joint works with Alexandru Chirvasitu, Sarah Reznikoff and Mariusz Tobolski.)

Tursday, 12. October 2019 - 10:15, room 602

Janusz Wysoczański

O pewnej C*-algebrze generowanej przez częściowe izometrie i spektrum jej maksymalnej C*-podalgebry abelowej

Operatory kreacji i anihilacji na słabo monotonicznej przestrzeni Focka są częściowymi izometriami. W referacie podam własności C*-algebry, którą generują. Opiszę także jej maksymalną abelową C*-podalgebrę (MASA). Dla tej MASA pokażę w jaki sposób można scharakteryzować jej przestrzeń Gelfanda czyli spektrum.

Tursday, 17. October 2019 - 10:15, room 602

Ryszard Szwarc

Closable Hankel forms and moment problems

In a paper from 2016 D. R. Yafaev considers Hankel operators associated with Hamburger moment sequences qn and claims that the corresponding Hankel form is closable if and only if the moment sequence tends to 0. The claim is not correct, since we prove closability for any indeterminate moment sequence but also for certain determinate moment sequences corresponding to measures with finite index of determinacy. It is also established that Yafaev’s result holds if the moments satisfy q1/(2n)2n = o(n).

Wednesday, 10.10.2019, 10:15-12:00, room 602

Marek Bożejko (IMPAN)

Positivity and Gaussian processes

We will present relations between positive definite kernels (also operator valued) and classical and quantum Gaussian processes following the paper of Yanqui Qiu - "On a result of Bozejko on extension of positive definite kernels" - arXiv - 2019 and Bull. London Math.Soc 2019 and the results of E.Hirai, T.Hirai and A.Hora and M.Guta and myself on Thoma representations of central positive definite functions on Coxeter groups of type A and B, i.e. on permutations group and sign-permutation group on infinite many letters.

Wednesday, 4.09.2019, 10:15-12:00, room 603
Vitonofrio Crismale (University of Bari Aldo Moro)
Sums and limit distribution for non symmetric weakly monotone position operators

In this talk we present the asymptotic vacuum distribution, under an appropriate scaling, of a family of partial sums of non-symmetric position operators on weakly monotone Fock space. This can be seen as the "Poisson type" limit measure in our setting. We preliminary show that any single operator has the vacuum law belonging to the free Meixner class. After establishing some relations between the combinatorics of Motzkin and Riordan paths, we give a recursive formula for the vacuum moments of the law of any partial sum. We exploit these results to achieve the asymptotic distribution as described above, which turns out to be indeed the sum of an atomic and an absolutely continuous part. Based on joint work with M.E. Griseta and J. Wysoczanski.


Seminar archives

Past schedule for the year 2018/2019
Past schedule for the year 2017/2018
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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