News
- Im Sommersemester 2025 wird Professor Speicher die Vorlesung “Funktionentheorie” halten. Die Anmeldung unter Moodle ist jetzt freigeschaltet.
- Roland Speicher and Alexander Wendel uploaded their new preprint “Entrywise application of non-linear functions on orthogonally invariant matrices” to the arXiv. An appetizer for this can also be found at the blog post "Understanding non-linearity in random matrices".
- The paper "Computing the Noncommutative Inner Rank by Means of Operator-Valued Free Probability Theory" by Johannes Hoffmann, Tobias Mai and Roland Speicher has now been published online in Foundations of Computational Mathematics. Here is a link to the open access article.
- In June 2024 Roland Speicher gave a lecture series of five 90 minutes talks on “Free Probability, Free Cumulants and Random Matrices” at the Beg Rohu Summer School on statistical physics. The lectures, which were intended as an introduction into the subject of free probability for physicists, were recorded and can be watched on youtube: lecture 1, lecture 2, lecture 3, lecture 4, lecture 5.
- A polished version of the lecture notes of the random matrix class has now appeared with EMS Press as Lectures on Random Matrices.
Online Resources
Some appetizer videos:
- Dan-Virgil Voiculescu: visionary operator algebraist and creator of free probability theory
- The curse and the blessing of high dimensions
- What is so amazing about Wigner's semircircle law?
- Why I prefer the Heisenberg picture over the Schrödinger picture
- Die wundersame Welt der Quantenmathematik: nicht-kommutative Wahrscheinlichkeiten
- Das seltsame zeitliche Verhalten von linearen Dglen bei nicht-orthogonalen Eigenvektoren
- Die Relevanz der komplexen Zahlen
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. [...]
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