Dear All, please find below an invitation for a talk in the Research Seminar Noncommutative and Functional Analysis.

Best regards, Roland Speicher

===================================================== Date: 27.11.2023

Time: 16:15

Place: HS IV, E2 4

Speaker: Petar Nizic-Nikolac (ETH Zürich)

Title: Non-asymptotic Link from Free Probability to Random Matrix Theory: Products of Gaussian Random Matrices

Abstract: One central question in Random Matrix Theory is to determine how the basic parameters of the model (dimension, structure, matrix variance...) impact more complicated properties (spectral norm, minimal eigenvalue, invertibility...). Answers to these questions often provide useful tools when analyzing stochastic algorithms. These tools can be assessed through three different categories: generality (of models/assumptions), sharpness, and asymptoticity. Specifically, to bound the spectral norm of a Gaussian random matrix, many tools are known, each exhibiting a different trade-off in these categories. Usually, these results are either non-asymptotic but with an additional logarithmic dependence on dimension or exact but asymptotical. A recent work by Bandeira, Boedihardjo, and van Handel presented both exact and non-asymptotic bounds for a general class of Gaussian random matrices. This was achieved by importing techniques from Free Probability that exactly capture non-commutativity on an intrinsic level. The talk will focus on using this non-asymptotic link to import other such techniques while increasing model generality, particularly for a product of Gaussian random matrices. This is joint work with Bandeira, van Handel, and Zeng.

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Webpage of the research seminar:

https://www.uni-saarland.de/lehrstuhl/weber-moritz/research/research-seminar...

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