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Outlier phenomena for deformed random band matrices
Probability| Speaker: | Benson Au, UC Berkeley |
| Related Webpage: | https://www.stat.berkeley.edu/~bensonau/ |
| Location: | 2112 MSB |
| Start time: | Mon, Feb 26 2024, 1:10PM |
A remarkable work of Benaych-Georges and Nadakuditi shows how one can understand the emergence of outliers in deformed random matrices using a weighted version of the eigenvalue distribution. Their results cover unitarily invariant random matrices, crucially using the fact that the eigenvectors of such matrices are Haar distributed (in particular, delocalized). In contrast, random band matrices are known to possess a localized phase. We study the outlier phenomenon for deformed random band matrices. Surprisingly, we find that the same outlier behavior persists into the localized phase. Our analysis relies on moment method calculations for general vector states.
Zoom: https://ucdavis.zoom.us/j/95654341648?pwd=Rkw3MU13UHAzT0R2RVZNMGpHYWk1QT09 Meeting ID: 956 5434 1648 Passcode: 910753