Asymptotic expansion for multiplicative statistics in a Hermitian matrix model connected to the lower tail of the KPZ equation

We explore the multiplicative statistics for a unitary random matrix ensemble with a parameter-dependent deformation inserted in the probability measure. Such deformations had been studied for a bounded or decaying parameter. In this work, we extend the previous results for a growing parameter under a controlled rate, and show that the underlying statistics relate to the lower tail study for the KPZ equation.