Autocorrelations of the characteristic polynomial of a random matrix under microscopic scaling

Rowan Killip, Eric Ryckman

Published 2010-04-09Version 1

We calculate the autocorrelation function for the characteristic polynomial of a random matrix in the microscopic scaling regime. While results fitting this description have be proved before, we will cover all values of inverse temperature $\beta \in (0,\infty)$. The method also differs from prior work, relying on matrix models introduced by Killip and Nenciu.