• Welcome to the Free Probability Group of Professor Roland Speicher at Saarland University.

      We have close collaborations with the groups of Professor Moritz Weber and Professor Michael Hartz.

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    • Moritz Weber

      Saarbrücken Quantum Group

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    • Michael Hartz

      Operator Theory and Complex Analysis Group

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News

Older News
  • Gaëtan Borot, Séverin Charbonnier, Elba Garcia-Failde, Felix Leid, and Sergey Shadrin have uploaded their new preprint on "Analytic theory of higher order free cumulants" to the archive; see also the post on the free probability blog.
  • Am 19. Juli um 19:30 Uhr hält Roland Speicher am Wissenschaftsforum MINT-Campus Alte Schmelz einen Vortrag zum Thema Nicht-kommutative Wahrscheinlichkeitstheorie und Zufallsmatritzen - das Wechselspiel zwischen abstrakter Theorie und konkreter Anwendung. Der Vortrag ist für ein allgemeines Publikum, Mathematiker dürfen aber auch gerne zuhören.
  • Zum Tag der offenen Tür stellen Professor Speicher und Professor Weber ihre Arbeitsgebiete aus der Quantenmathematik in zwei kleinen Videos vor: nicht-kommutative Wahrscheinlichkeiten (Speicher) und nicht-kommutative Symmetrien (Weber).
  • Die noch ausstehenden Videos der Vorlesung HMI 3 sind nun online zugänglich, sowohl unter Moodle wie auch im youtube Kanal. Damit ist der Video-Zyklus für die HMI beendet. Für die HMI 4 Vorlesungen wird es keine Videos geben.
  • The Queen's Seminar on Free Probability and Random Matrices is now running online; see also the announcement on the free probability blog.
  • Octavio Arizmendi, Guillaume Cebron, Roland Speicher and Sheng Yin have just uploaded their new paper “Universality of free random variables: atoms for non-commutative rational functions“ to the archive. For an appetizer see the blog entry, for the full meal go directly to the preprint.
  • Roland Speicher gave a mini-course of three talks on the relation between higher order freeness and topological recursion at the conference Noncommutative geometry meets topological recursion in Münster. All talks were recorded and can be found on the youtube playlist of the conference.
  • Since March 1, 2021, Moritz Weber is a Heisenberg professor at Saarland University - see the press release (in German). Congratulations to Moritz!
  • The talk "What actually is free probability theory?" by Tobias Mai at the Technion was recorded and can be found here on youtube.
  • The talk "Singularity of matrices in non-commuting variables and free probability" by Roland Speicher at the Technion was recorded and can be found here on youtube.
  • A PhD position, funded by the DFG, on a project "Free Probability Aspects of Neural Networks" is available - if you are interested see here for details.
  • Michael Hartz has been awarded the Barbara and Jaroslav Zemánek Prize (see announcement  and a personal laudatio in the blog of Orr Shalit). This is given to young researchers for achievements in functional analysis, with special emphasis on operator theory. Congratulations to Michael!
  • Roland Speicher will give a colloquium talk at the Math Department of the Technion, Israel on Monday, January 25 – online, of course. They have the nice option of a pre-colloquium talk, which provides students with some background for the material appearing in the colloquium talk. Tobias Mai agreed to give such a preparation talk. So he will give on Thursday, January 21, an introduction to free probability and its relation with random matrices. Surely a great opportunity for everyone to learn (more) about the subject. See here for more info.
  • Moritz Weber was selected for the Heisenberg programme of the German Research Foundation. His own position will be fully funded from early 2021 for five years. That's a great achievement. Congratulations to Moritz!
  • Daniel Gromada finished his PhD in September 2020.
  • The Lecture Notes on Non-Commutative Distributions (course from summer term 2019) are now online.
  • Simon Schmidt finished his PhD in July 2020.
  • The talk of Roland Speicher on "Random matrices and their limits" in the Wales MPPM Seminar is now online. May 12, 2020.
  • The videos of the three talks of Roland Speicher in the Distinguished Lecture Series at the Fields Institute are now online.
  • Miguel Pluma and Sheng Yin finished their PhD in January 2020.
  • Stefan Jung finished his PhD in June 2019.

Our guests

Information for our visitors

On this page you will find some information concerning a stay at Saarbrücken, at our research group on Free Probability Theory, Random Matrices, and Quantum Groups. If you have any suggestions or comments about this site, please help us to improve it!

Download the main information of this page (including the campus map) here.

 

ERC Advanced Grant

From 1 February 2014 until 31 January 2019, the European Research Council supported the research of Roland Speicher by an ERC Advanced Grant with the title Non-Commutative Distributions in Free Probability. More info on this can be found here

SFB-TRR 195

Symbolic Tools in Mathematics and their Application

The Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) has established the transregional collaborative research centre (SFB-TRR) 195 “Symbolic Tools in Mathematics and their Application” starting in January 2017.  Host university is the University of Kaiserslautern (TU Kaiserslautern), additional applicant universities are RWTH Aachen University and Saarland University.

What actually is Free Probability?

A motivating example

Consider the following three natural questions from the fields of operator algebras, random matrices, and combinatorics, respectively.

  • What is the distribution of the real part of the one-sided shift with respect to the canonical vacuum expectation state?
  • What is the asymptotic eigenvalue distribution of a Gaussian random matrix in the limit of large matrix size?
  • In how many ways can one connect 2n points on a circle pairwisely by n non-intersecting chords?

Surprisingly, all three questions have essentially the same answer: both question 1 and 2 yield the semicircular distribution, and the answer to question 3 is given by the Catalan numbers which are actually the even moments of the semicircular distribution. This coincidence is not just superficial - a conceptual reason is given by Voiculescu's free probability theory and its basic concept of freeness. [...]

Postal address

Saarland University
Department of Mathematics
Postfach 15 11 50
66041 Saarbrücken
Germany

 

Visitors

Saarland University
Campus building E 2 4
66123 Saarbrücken
Germany