Linear Eigenvalue statistics at the cusp
Download (ext.)
Journal Article
| Epub ahead of print
| English
Scopus indexed
Author
Corresponding author has ISTA affiliation
Department
Abstract
We establish universal Gaussian fluctuations for the mesoscopic linear eigenvalue statistics in the vicinity of the cusp-like singularities of the limiting spectral density for Wigner-type random matrices. Prior to this work, the linear eigenvalue statistics at the cusp-like singularities were not studied in any ensemble. Our analysis covers not only the exact cusps but the entire transitionary regime from the square-root singularity at a regular edge through the sharp cusp to the bulk. We identify a new one-parameter family of functionals that govern the limiting bias and variance, continuously interpolating between the previously known formulas in the bulk and at a regular edge. Since cusps are the only possible singularities besides the regular edges, our result gives a complete description of the linear eigenvalue statistics in all regimes.
Publishing Year
Date Published
2025-04-15
Journal Title
Probability Theory and Related Fields
Publisher
Springer Nature
Acknowledgement
I would like to express my gratitude to László Erdős for his careful guidance and supervision of my work. I am also thankful to Jana Reker and Joscha Henheik for many helpful discussions. Open access funding provided by Institute of Science and Technology (IST Austria).
ISSN
eISSN
IST-REx-ID
All files available under the following license(s):
Creative Commons Attribution 4.0 International Public License (CC-BY 4.0):
Link(s) to Main File(s)
Access Level

Export
Marked PublicationsOpen Data ISTA Research Explorer
Sources
arXiv 2307.07432