Abstract
In this paper we show, how a straightforward and natural application of a pair of fundamental identities valid for polynomials orthogonal over the unit circle, can be used to calculate the determinant of the finite Toeplitz matrix Δ n , with the Fisher-Hartwig symbol. We use the same approach to compute a difference equation for expressions related to the determinants of symbols that have important application in the study of random permutations.
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E.L. Basor was supported in part by National Science Foundation grant DMS-0200167 and also in part by the EPSRC for a Visiting Fellowship.
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Basor, E.L., Chen, Y. Toeplitz determinants from compatibility conditions. Ramanujan J 16, 25–40 (2008). https://doi.org/10.1007/s11139-007-9090-0
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DOI: https://doi.org/10.1007/s11139-007-9090-0