scholarly journals Asymptotics of a cubic sine kernel determinant

2015 ◽  
Vol 26 (4) ◽  
pp. 515-565
Author(s):  
T. Bothner ◽  
A. Its
Keyword(s):  
Sine Kernel

scholarly journals Universality of Sine-Kernel for Wigner Matrices with a Small Gaussian Perturbation

2010 ◽  
Vol 15 (0) ◽  
pp. 526-604 ◽  
Author(s):  
Laszlo Erdos ◽  
Jose Ramirez ◽  
Benjamin Schlein ◽  
Horng-Tzer Yau
Keyword(s):  
Wigner Matrices ◽  
Gaussian Perturbation ◽  
Sine Kernel

Boundaries of sine kernel universality for Gaussian perturbations of Hermitian matrices

2019 ◽  
Vol 08 (03) ◽  
pp. 1950011 ◽  
Author(s):  
Tom Claeys ◽  
Thorsten Neuschel ◽  
Martin Venker
Keyword(s):  
Brownian Motion ◽  
Initial Data ◽  
Interior Point ◽  
Initial Density ◽  
Time Span ◽  
Hermitian Matrices ◽  
Sine Kernel

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.

scholarly journals The top eigenvalue of the random Toeplitz matrix and the sine kernel

2013 ◽  
Vol 41 (6) ◽  
pp. 4050-4079 ◽  
Author(s):  
Arnab Sen ◽  
Bálint Virág
Keyword(s):  
Toeplitz Matrix ◽  
Sine Kernel

scholarly journals Riemann–Hilbert approach to a generalized sine kernel

2019 ◽  
Vol 110 (2) ◽  
pp. 297-325
Author(s):  
Roozbeh Gharakhloo ◽  
Alexander R. Its ◽  
Karol K. Kozlowski
Keyword(s):  
Sine Kernel
Sign in / Sign up

Export Citation Format

Share Document