Eigenvectors of Ginibre matrices

Combinatorics Seminar
Event time: 
Thursday, September 26, 2019 - 3:00pm
DL 316
Paul Bourgade
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Eigenvectors of non-Hermitian matrices are typically non-orthogonal, and their distance to a unitary basis can be quantified through the matrix of overlaps. These variables quantify the stability of the spectrum. They first appeared in the physics literature; well known work by Chalker and Mehlig calculated the expectation of these overlaps for complex Ginibre matrices. For the same model, we extend their results by deriving the distribution of the overlaps and their correlations. Some results are based on an explicit solvable P-recursive equation, for which conceptual understanding is lacking. (Joint work with Guillaume Dubach).

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