Abstract
AbstractWe obtain an asymptotic formula for $$n\times n$$
n
×
n
Toeplitz determinants as $$n\rightarrow \infty $$
n
→
∞
, for non-negative symbols with any fixed number of Fisher–Hartwig singularities, which is uniform with respect to the location of the singularities. As an application, we prove a conjecture by Fyodorov and Keating (Philos Trans R Soc A 372: 20120503, 2014) regarding moments of averages of the characteristic polynomial of the Circular Unitary Ensemble. In addition, we obtain an asymptotic formula regarding the momentum of impenetrable bosons in one dimension with periodic boundary conditions.
Funder
Leverhulme Trust
Göran Gustafssons Stiftelse för Naturvetenskaplig och Medicinsk Forskning
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
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