Optimal multi-resolvent local laws for Wigner matrices
Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38.
Download
Journal Article
| Published
| English
Scopus indexed
Corresponding author has ISTA affiliation
Department
Abstract
We prove local laws, i.e. optimal concentration estimates for arbitrary products of resolvents of a Wigner random matrix with deterministic matrices in between. We find that the size of such products heavily depends on whether some of the deterministic matrices are traceless. Our estimates correctly account for this dependence and they hold optimally down to the smallest possible spectral scale.
Publishing Year
Date Published
2022-09-12
Journal Title
Electronic Journal of Probability
Publisher
Institute of Mathematical Statistics
Acknowledgement
L. Erdős was supported by ERC Advanced Grant “RMTBeyond” No. 101020331. D. Schröder was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.
Volume
27
Page
1-38
eISSN
IST-REx-ID
Cite this
Cipolloni G, Erdös L, Schröder DJ. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 2022;27:1-38. doi:10.1214/22-ejp838
Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-ejp838
Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/22-ejp838.
G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal multi-resolvent local laws for Wigner matrices,” Electronic Journal of Probability, vol. 27. Institute of Mathematical Statistics, pp. 1–38, 2022.
Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38.
Cipolloni, Giorgio, et al. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” Electronic Journal of Probability, vol. 27, Institute of Mathematical Statistics, 2022, pp. 1–38, doi:10.1214/22-ejp838.
All files available under the following license(s):
Creative Commons Attribution 4.0 International Public License (CC-BY 4.0):
Main File(s)
File Name
2022_ElecJournProbability_Cipolloni.pdf
502.15 KB
Access Level
Open Access
Date Uploaded
2023-01-30
MD5 Checksum
bb647b48fbdb59361210e425c220cdcb
Export
Marked PublicationsOpen Data ISTA Research Explorer
Google Scholar