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Asymptotic expansion of Toeplitz determinants of an indicator function with discrete rotational symmetry and powers of random unitary matrices by Marchal, Olivier is a scholarly article available to read on EtoBox.

What is Asymptotic expansion of Toeplitz determinants of an indicator function with discrete rotational symmetry and powers of random unitary matrices about?

In this short article we propose a full large $N$ asymptotic expansion of the probability that the $m^{\text{th}}$ power of a random unitary matrix of size $N$ has all its eigenvalues in a given arc-interval centered in $1$ when $N$ is large. This corresponds to the asymptotic expansion of a Toeplitz determinant whose symbol is the indicator function of several intervals having a discrete rotational symmetry. This solves and improves a conjecture left opened by the author. It also provides a rare example of the explicit computation of a full asymptotic expansion of a genus $g>0$ classical spectral curve, including the oscillating non-perturbative terms, using the topological recursion.

Author

Marchal, Olivier

Published

2021

Language

EN