Cusp universality for random matrices II: The real symmetric case

G. Cipolloni, L. Erdös, T.H. Krüger, D.J. Schröder, ArXiv (n.d.).

Preprint | Submitted | English
Department
Abstract
We prove that the local eigenvalue statistics of real symmetric Wigner-type matrices near the cusp points of the eigenvalue density are universal. Together with the companion paper [arXiv:1809.03971], which proves the same result for the complex Hermitian symmetry class, this completes the last remaining case of the Wigner-Dyson-Mehta universality conjecture after bulk and edge universalities have been established in the last years. We extend the recent Dyson Brownian motion analysis at the edge [arXiv:1712.03881] to the cusp regime using the optimal local law from [arXiv:1809.03971] and the accurate local shape analysis of the density from [arXiv:1506.05095, arXiv:1804.07752]. We also present a PDE-based method to improve the estimate on eigenvalue rigidity via the maximum principle of the heat flow related to the Dyson Brownian motion.
Publishing Year
Date Published
2018-11-09
Journal Title
arXiv
Page
60
IST-REx-ID

Cite this

Cipolloni G, Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices II: The real symmetric case. arXiv.
Cipolloni, G., Erdös, L., Krüger, T. H., & Schröder, D. J. (n.d.). Cusp universality for random matrices II: The real symmetric case. ArXiv.
Cipolloni, Giorgio, László Erdös, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices II: The Real Symmetric Case.” ArXiv, n.d.
G. Cipolloni, L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices II: The real symmetric case,” arXiv. .
Cipolloni G, Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices II: The real symmetric case. arXiv.
Cipolloni, Giorgio, et al. “Cusp Universality for Random Matrices II: The Real Symmetric Case.” ArXiv.

Link(s) to Main File(s)
Access Level
OA Open Access
Material in IST:
Dissertation containing IST record

Export

Marked Publications

Open Data IST Research Explorer

Sources

arXiv 1811.04055

Search this title in

Google Scholar