An edge CLT for the log determinant of Laguerre beta ensembles

Elizabeth Collins-Woodfin, Han Gia Le

We obtain a CLT for $\log |\det (M_n-s_n)|$ where $M_n$ is a scaled Laguerre $\beta$ ensemble and $s_n=d_{+}+{\sigma }_n{n}^{-2/3}$ with $d_{+}$ denoting the upper edge of the limiting spectrum of $M…