Benoît Collins
(University of Kyoto)
March 29, 2021
Organized by Asia-Pacific GNCG Seminar.

Matrix models for non-commutative rational functions

We will report on arXiv:2103.05962, written in collaboration with Tobias Mai, Akihiro Miyagawa, Felix Parraud and Sheng Yin. Random matrix models in the multi-matrix setup focus primarily on the study of non-commutative polynomials in multiple matrix valued random variables and aim at studying their behavior in the limit of large dimension. We show that this study can be extended to the context of non-commutative rational fractions, hereby uncovering a broad new class of converging unbounded matrix models, and answering an open question of Roland Speicher. 

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