Fall 2024 reading group
Free probability theory + matrix inequalities and spectral graph theory
This page collects material I compiled over the course of a reading group in Prof. Lap Chi Lau’s group during the Fall 2024 semester. The reading group itself was aimed at understanding a result on improved matrix concentration inequalities by van Handel, using free probability theory (FPT).
- Proof of continuous functional calculus
- Typeset notes accompanying a presentation on the R-transform, free convolutions, products of free elements
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- A previous version of these notes had an error in Proposition 2.7. This has now been fixed.
- Typset notes accompanying a presentation introducing operator-valued FPT
- (To be added next weekend) Notes on computing the norm of a free operator on Fock space via FPT
- (To be added this weekend) Notes for a presentation on Gaussian random matrices and intro to strong convergence