Large deviations principle for the largest eigenvalue of Wigner matrices without Gaussian tails

By F. Augeri. 2015

46 citations recorded by the source corpus.

We prove a large deviation principle for the largest eigenvalue of Wigner matrices without Gaussian tails, namely such that the distribution tails $\mathbb{P}( |X_{1,1}|>t)$ and $\mathbb{P}(|X_{1,2}|>t)$ behave like $e^{-bt^{\alpha}}$ and $e^{-at^{\alpha}}$ respectively for some $a,b\in (0,+\infty)$ and $\alpha\in (0,2)$. The large deviation principle is of speed $N^{\alpha/2}$ and with a good rate function depending only on the tail distribution of the entries.

Subfields: Geometry and Topology, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/80feb202c5bb84915831a61f9ff73dbfaefc0e85