Uniform Asymptotics of Toeplitz Determinants with Fisher–Hartwig Singularities

Abstract We obtain an asymptotic formula for $$n\times n$$ n × Toeplitz determinants as $$n\rightarrow \infty $$ → ∞ , non-negative symbols with any fixed number of Fisher–Hartwig singularities, which is uniform respect to the location singularities. As application, we prove a conjecture by Fyodorov and Keating (Philos Trans R Soc A 372: 20120503, 2014) regarding moments averages characteristic polynomial Circular Unitary Ensemble. In addition, momentum impenetrable bosons in one dimension periodic boundary conditions.