An edge CLT for the log determinant of Laguerre beta ensembles

2022/09/07 by Elizabeth W Collins-Woodfin, Collins-Woodfin, Elizabeth, Han Gia Le +1 · 1 citation
Mathematics · Physics and Astronomy · #60B20 #60F05 #Advanced Combinatorial Mathematics #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2209.03271

openalex publication_date 2022/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain a CLT for log|det(M_n-s_n)| where M_n is a scaled Laguerre β ensemble and s_n=d₊+σ_n n^-2/3 with d₊ denoting the upper edge of the limiting spectrum of M_n and σ_n a slowly growing function (loglog² n≪σ_n≪log² n). In the special cases of LUE and LOE, we prove that the CLT also holds for σ_n of constant order. 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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