Boundaries of sine kernel universality for Gaussian perturbations of Hermitian matrices

Claeys T, Neuschel T, Venker M (2019)
Random Matrices: Theory and Applications 8(3): 1950011.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurde kein Volltext hochgeladen. Nur Publikationsnachweis!
Autor/in
; ;
Abstract / Bemerkung
We explore the boundaries of sine kernel universality for the eigenvalues of Gaussian perturbations of large deterministic Hermitian matrices. Equivalently, we study for deterministic initial data the time after which Dyson's Brownian motion exhibits sine kernel correlations. We explicitly describe this time span in terms of the limiting density and rigidity of the initial points. Our main focus lies on cases where the initial density vanishes at an interior point of the support. We show that the time to reach universality becomes larger if the density vanishes faster or if the initial points show less rigidity.
Stichworte
Random matrices; sine kernel; universality; Dyson's Brownian motion
Erscheinungsjahr
2019
Zeitschriftentitel
Random Matrices: Theory and Applications
Band
8
Ausgabe
3
Art.-Nr.
1950011
ISSN
2010-3263
eISSN
2010-3271
Page URI
https://pub.uni-bielefeld.de/record/2936943

Zitieren

Claeys T, Neuschel T, Venker M. Boundaries of sine kernel universality for Gaussian perturbations of Hermitian matrices. Random Matrices: Theory and Applications. 2019;8(3): 1950011.
Claeys, T., Neuschel, T., & Venker, M. (2019). Boundaries of sine kernel universality for Gaussian perturbations of Hermitian matrices. Random Matrices: Theory and Applications, 8(3), 1950011. doi:10.1142/S2010326319500114
Claeys, T., Neuschel, T., and Venker, M. (2019). Boundaries of sine kernel universality for Gaussian perturbations of Hermitian matrices. Random Matrices: Theory and Applications 8:1950011.
Claeys, T., Neuschel, T., & Venker, M., 2019. Boundaries of sine kernel universality for Gaussian perturbations of Hermitian matrices. Random Matrices: Theory and Applications, 8(3): 1950011.
T. Claeys, T. Neuschel, and M. Venker, “Boundaries of sine kernel universality for Gaussian perturbations of Hermitian matrices”, Random Matrices: Theory and Applications, vol. 8, 2019, : 1950011.
Claeys, T., Neuschel, T., Venker, M.: Boundaries of sine kernel universality for Gaussian perturbations of Hermitian matrices. Random Matrices: Theory and Applications. 8, : 1950011 (2019).
Claeys, Tom, Neuschel, Thorsten, and Venker, Martin. “Boundaries of sine kernel universality for Gaussian perturbations of Hermitian matrices”. Random Matrices: Theory and Applications 8.3 (2019): 1950011.