# On lacunary Toeplitz determinants

Source: [On lacunary Toeplitz determinants](<https://www.sota2.com/research/paper/68fa50881e209131ce96c2a2>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T10:54:35.159Z

Authors: K. K. Kozlowski

Published: 2013-10-09T19:01:30.000Z

## Abstract

By using Riemann--Hilbert problem based techniques, we obtain the asymptotic expansion of lacunary Toeplitz determinants $\\det\_N\\big\[ c\_{\\ell\_a-m\_b}\[f\] \\big\]$ generated by holomorhpic symbols, where $\\ell\_a=a$ (resp. $m\_b=b$) except for a finite subset of indices $a=h\_1,\\dots, h\_n$ (resp. $b=t\_1,\\dots, t\_r$). In addition to the usual Szeg\\"{o} asymptotics, our answer involves a determinant of size $n+r$.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1310.2584>)

[PDF](<https://arxiv.org/pdf/1310.2584.pdf>)