Han Gia Le, University of Michigan
Authors: Elizabeth Collins-Woodfin, Han Gia Le
2023 AWM Research Symposium
Poster Presentation

We obtain a CLT for the logarithm of $|\rm{det}(M_n − s_n)|$ where $M_n$ is a scaled Laguerre beta ensemble and $s_n$ is near the upper edge of the limiting spectrum of the matrix. In the special cases of Laguerre orthogonal and unitary ensembles, the lower bound on $s_n$ can be relaxed. A similar result was proved for Wigner matrices by Johnstone, Klochkov, Onatski, and Pavlyshyn. Obtaining this type of CLT of Laguerre matrices is of interest for statistical testing of critically spiked sample covariance matrices as well as free energy of bipartite spherical spin glasses at critical temperature.

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