Wednesday, October 13, 2021 - 09:00 in ZOOM - Video Conference
Local Marchenko-Pastur law on the optimal scale
A talk in the Seminar Zufallsmatrizen series by
Anna Maltsev from Queen Mary University, London
| Abstract: |
Consider an N by N matrix X of complex entries with iid real and imaginary parts. We show that the local density of eigenvalues of X*X converges to the Marchenko-Pastur law on the optimal scale with probability 1. We also obtain rigidity of the eigenvalues in the bulk and near both hard and soft edges. Here we avoid logarithmic and polynomial corrections by working directly with high powers of expectation of the Stietjes transforms. We work under two sets of assumptions: either the entries have bounded moments or the entries have a finite 4th moment and are truncated at N^(1/4). In this work we simplify and adapt the methods from prior papers of Götze-Tikhomirov and Cacciapuoti-Maltsev-Schlein to covariance matrices. This is joint work with Anastasis Kafetzopoulos.
Please contact Anas Rahman (anas.rahman@live.com.au) for details regarding access.
Within the CRC this talk is associated to the project(s): C6 |
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