We consider the least singular value of a large random matrix with real or complex i.i.d. Gaussian entries shifted by a constant z 2 C. We prove an optimal lower tail estimate on this singular value in the critical regime where z is around the spectral edge, thus improving the classical bound of Sankar, Spielman and Teng (SIAM J. Matrix Anal. Appl. 28:2 (2006), 446-476) for the particular shift-perturbation in the edge regime. Lacking Brézin-Hikami formulas in the real case, we rely on the superbosonization formula.
Cipolloni, G., Erdős, L., Schroder, D. (2022). Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble. PROBABILITY AND MATHEMATICAL PHYSICS, 1(1), 101-146 [10.2140/PMP.2020.1.101].
Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble
Cipolloni, Giorgio;
2022-01-01
Abstract
We consider the least singular value of a large random matrix with real or complex i.i.d. Gaussian entries shifted by a constant z 2 C. We prove an optimal lower tail estimate on this singular value in the critical regime where z is around the spectral edge, thus improving the classical bound of Sankar, Spielman and Teng (SIAM J. Matrix Anal. Appl. 28:2 (2006), 446-476) for the particular shift-perturbation in the edge regime. Lacking Brézin-Hikami formulas in the real case, we rely on the superbosonization formula.| File | Dimensione | Formato | |
|---|---|---|---|
|
unpaywall-bitstream--1888316152.pdf
solo utenti autorizzati
Tipologia:
Versione Editoriale (PDF)
Licenza:
Copyright dell'editore
Dimensione
3.73 MB
Formato
Adobe PDF
|
3.73 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
