Local law for random gram matrices

Alt J, Erdos L, Krueger T (2017)

Publication Type: Journal article

Publication year: 2017


Book Volume: 22

Article Number: 25

DOI: 10.1214/17-EJP42


We prove a local law in the bulk of the spectrum for random Gram matrices XX*, a generalization of sample covariance matrices, where X is a large matrix with independent, centered entries with arbitrary variances. The limiting eigenvalue density that generalizes the Marchenko-Pastur law is determined by solving a system of nonlinear equations. Our entrywise and averaged local laws are on the optimal scale with the optimal error bounds. They hold both in the square case (hard edge) and in the properly rectangular case (soft edge). In the latter case we also establish a macroscopic gap away from zero in the spectrum of XX*.

Authors with CRIS profile

Involved external institutions

How to cite


Alt, J., Erdos, L., & Krueger, T. (2017). Local law for random gram matrices. Electronic Journal of Probability, 22. https://doi.org/10.1214/17-EJP42


Alt, Johannes, Laszlo Erdos, and Torben Krueger. "Local law for random gram matrices." Electronic Journal of Probability 22 (2017).

BibTeX: Download