Proves Fredholm determinantal identity for tilted Toeplitz minors generalizing BOGC, with bialternant forms, Cauchy-Binet expansions, and asymptotic links to Airy kernel perturbations.
On lacunary Toeplitz determinants
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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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math.FA 1years
2026 1verdicts
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A Borodin-Okounkov-Geronimo-Case identity for tilted Toeplitz minors
Proves Fredholm determinantal identity for tilted Toeplitz minors generalizing BOGC, with bialternant forms, Cauchy-Binet expansions, and asymptotic links to Airy kernel perturbations.