Title: Birth of a cut in unitary random matrix ensembles
Authors: Claeys, Tom # ×
Issue Date: 2008
Publisher: Duke University Press
Series Title: International Mathematics Research Notices vol:2008 issue:6
Article number: rnm166
Abstract: We study unitary random matrix ensembles in the critical regime where a new cut arises away from the original spectrum. We perform a double scaling limit where the size of the matrices tends to infinity, but in such a way that only a bounded number of eigenvalues is expected in the newborn cut. It turns out that limits of the eigenvalue correlation kernel are given by Hermite kernels corresponding to a finite size Gaussian unitary ensemble (GUE). When modifying the double scaling limit slightly, we observe a remarkable transition each time the new cut picks up an additional eigenvalue, leading to a limiting kernel interpolating between GUE-kernels for matrices of size k and size k + 1. We prove our results using the Riemann–Hilbert approach.
ISSN: 1073-7928
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

Files in This Item:

There are no files associated with this item.

Request a copy


All items in Lirias are protected by copyright, with all rights reserved.

© Web of science