Secular coefficients and the holomorphic multiplicative chaos
Secular coefficients and the holomorphic multiplicative chaos
We study the secular coefficients of N×N random unitary matrices UN drawn from the Circular β-Ensemble which are defined as the coefficients of {zn} in the characteristic polynomial det(1−zUN∗). When β>4, we obtain a new class of limiting distributions that arise when both n and N tend to infinity simultaneously. …