# Fluctuations at the edges of the spectrum of the full rank deformed GUE

Abstract : We consider a full rank deformation of the GUE $W_N+A_N$ where $A_N$ is a full rank Hermitian matrix of size $N$ and $W_N$ is a GUE. The empirical eigenvalue distribution $\mu_{A_N}$ of $A_N$ converges to a probability distribution $\nu$. We identify all the possible limiting eigenvalue statistics at the edges of the spectrum, including outliers, edges and merging points of connected components of the limiting spectrum. The results are stated in terms of a deterministic equivalent of the empirical eigenvalue distribution of $W_N+A_N$, namely the free convolution of the semi-circle distribution and the empirical eigenvalues distribution of $A_N$.
Type de document :
Article dans une revue
Probability Theory and Related Fields, Springer Verlag, 2016, 165 (1), pp.117-161. 〈10.1007/s00440-015-0628-6〉
Domaine :

https://hal.archives-ouvertes.fr/hal-01011501
Contributeur : Mireille Capitaine <>
Soumis le : mardi 24 juin 2014 - 09:41:03
Dernière modification le : vendredi 4 janvier 2019 - 17:32:33

### Citation

Mireille Capitaine, S. Péché. Fluctuations at the edges of the spectrum of the full rank deformed GUE. Probability Theory and Related Fields, Springer Verlag, 2016, 165 (1), pp.117-161. 〈10.1007/s00440-015-0628-6〉. 〈hal-01011501〉

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