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Sarah Timhadjelt

Second largest eigenvalue of the sum of a deterministic matrix and a random permutation
Tuesday, 30 January, 2024 - 15:30 to 16:30
Résumé : 

We consider a random bistochastic matrix of size $N$ of the form $(1-r)M + rQ$ where $0<r<1$, $M$ is a uniformly distributed permutation and $Q$ is a given bistochastic matrix. Under sparsity and regularity assumptions on the $*$-distribution of $Q$ (that is the normalized trace of polynomials in $Q$ and $Q^*$), we prove that the second largest eigenvalue of $(1-r)M + rQ$ is essentially bounded by an approximation of the spectral radius of a deterministic asymptotic equivalent given by free probability theory. This upper-bound has application in graph theory, for instance for the construction of graph expander.

Institution de l'orateur : 
I2M, Marseille
Thème de recherche : 
Probabilités
Salle : 
4
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