Roland Speicher

Professor Dr.

Michael Hartz

JProfessor Dr.

Moritz Weber

Professor Dr.



  • 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).
  • 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; applications deadline is June 20, 2021.
  • 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.
Older News
  • 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.

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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!

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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


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
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66041 Saarbrücken



Saarland University
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