A CLT for the characteristic polynomial of random Jacobi matrices, and the G$\beta$E

Abstract

We prove a central limit theorem for the logarithm of the characteristic polynomial of random Jacobi matrices. Our results cover the G$\beta$E models for $\beta >0$.

arXiv commentV3: Corrected a mistake in computation of centering, improved error estimates through section 4, various typos corrected. V4: Slight modifications and rearrangement, to appear in PTRF