Eigenvectors of integrable models of non-Hermitian random matrices
Date
Tuesday, August 20, 2019 10:00 - 12:00
Speaker
Guillaume Dubach (CIMS, New York University)
Location
Heinzel Seminar Room / Office Bldg West (I21.EG.101)
Series
Seminar/Talk
Tags
Mathematics and CS Seminar, mathematical_seminar_ics
Host
László Erdös
Contact
Right and left eigenvectors of non-Hermitian matrices form a bi-orthogonal system, to which one can associate homogeneous quantities known as overlaps. The matrix of overlaps quantifies the stability of the spectrum, and characterizes the joint eigenvalues increments under Dyson-type dynamics. Overlaps first appeared in the physics literature: Chalker and Mehlig calculated their conditional expectation for complex Ginibre matrices (1998). For the same model, we extend their results by deriving the distribution of the overlaps and their correlations (joint work with P. Bourgade). Similar results hold for quaternionic Gaussian matrices, as well as matrices from the spherical and truncated unitary ensembles.