Spectral distribution of tensor products of random matrices.
Patrick OLIVEIRA SANTOS
New York University Abu Dhabi
Date(s) : 31/03/2026 iCal
14h30 - 15h30
In this talk, I will discuss the spectral distribution of tensor products of random matrices. While random matrices can often be viewed as noncommutative operators, tensor products introduce additional commutation relations that modify the resulting spectral structure.
We use graphs to encode the commutation relations among the matrices. In the high-order regime, the limiting spectral distribution can be described through the graphon limit of these graphs.
From this graph-theoretic perspective, we obtain a family of graphon-driven limiting laws interpolating between classical and free behavior. This includes the Gaussian and semicircle distributions and recovers earlier tensor-free central limit theorems.
If time permits, I will also discuss several open problems and ongoing projects related to this framework. This talk is based on joint work with Cécilia Lancien, Pierre Youssef, Guillaume Cébron, and Raghavendra Tripathi
Emplacement
I2M Saint-Charles - Salle de séminaire
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