Truncated Wiener-Hopf operators with Fisher Hartwig singularities

Abstract

We derive the asymptotic behavior of determinants of truncated Wiener-Hopf operators generated by symbols having Fisher-Hartwig singularities. This task is achieved thanks to an asymptotic resolution of the Riemann-Hilbert problem associated to some generalized sine kernel. As a byproduct, we give yet another derivation of the asymptotic behavior of Toeplitz determinants having Fisher-Hartwig singularities. The Riemann-Hilbert problem approach to these asymptotics yields a systematic although quickly cumbersome way to compute their sub-leading asymptotics.

68 pages (V3, minor corrections)

References in corpus (3)

• Riemann-Hilbert approach to a generalized sine kernel and applications
• Asymptotics for Toeplitz determinants on a circular arc
• Toeplitz and Hankel determinants with singularities: announcement of results

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• Riemann-Hilbert approach to a generalized sine kernel and applications
• Emptiness formation probability, Toeplitz determinants, and conformal field theory
• Exact full counting statistics for the staggered magnetization and the domain walls in the XY spin chain
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