Toeplitz and Hankel determinants with singularities: announcement of results
P. Deift, A. Its, I. Krasovsky
TL;DR
This paper presents new asymptotic results for Toeplitz, Hankel, and combined determinants with symbols exhibiting Fisher-Hartwig singularities, advancing understanding in this mathematical area.
Contribution
It introduces novel asymptotic formulas for determinants with singular symbols, expanding the theoretical framework for Toeplitz and Hankel matrices.
Findings
Asymptotic formulas for determinants with Fisher-Hartwig singularities
Extension of existing results to combined Toeplitz+Hankel determinants
Foundational results to be detailed in future publication
Abstract
We obtain asymptotics for Toeplitz, Hankel, and Toeplitz+Hankel determinants whose symbols possess Fisher-Hartwig singularities. Details of the proofs will be presented in another publication.
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Taxonomy
TopicsRandom Matrices and Applications · Advanced Combinatorial Mathematics · Mathematical functions and polynomials