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• W3206021787 abstract "We consider fluctuations of the largest eigenvalues of the random matrix model $A+UBU^{*}$ where $A$ and $B$ are $(Ntimes N)$ deterministic Hermitian matrices and $U$ is a Haar-distributed unitary matrix. Our main result is that the law of the largest eigenvalue weakly converges to the Tracy-Widom distribution, under mild assumptions on $A$ and $B$ to guarantee that the density of states of the model decays as square root around the upper edge. We apply Green function comparison method to the Dyson Brownian motion starting from the matrix $A+UBU^{*}$ and ending at time $N^{-1/3+chi}$. As a byproduct of our proof, we also prove an optimal local law for the Dyson Brownian motion up to the constant time scale." @default.
• W3206021787 created "2021-10-25" @default.
• W3206021787 creator A5053003491 @default.
• W3206021787 creator A5089051083 @default.
• W3206021787 date "2021-10-11" @default.
• W3206021787 modified "2023-09-27" @default.
• W3206021787 title "Tracy-Widom limit for free sum of random matrices" @default.
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• W3206021787 hasPublicationYear "2021" @default.
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