Abstract
In this article we consider Wigner matrices with variance profiles which are of the form where σ is a symmetric real positive function of , either continuous or piecewise constant and where the are independent, centered of variance one above the diagonal. We prove a large deviation principle for the largest eigenvalue of those matrices under the condition that they have sharp sub-Gaussian tails and under some additional assumptions on σ. These sub-Gaussian bounds are verified for example for Gaussian variables, Rademacher variables or uniform variables on . This result is new even for Gaussian entries.
Funding Statement
This work was partially supported by ERC Project LDRAM: ERC-2019-ADG Project 884584.
Citation
Jonathan Husson. "Large deviations for the largest eigenvalue of matrices with variance profiles." Electron. J. Probab. 27 1 - 44, 2022. https://doi.org/10.1214/22-EJP793
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