On a conjecture of Widom

Alexei Borodin; Alexei Novikov

doi:10.1088/0305-4470/39/28/S07

On a conjecture of Widom

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Abstract

We prove a conjecture of Widom (2002 Int. Math. Res. Not. 455-64 (Preprint math/0108008)) about the reality of eigenvalues of certain infinite matrices arising in asymptotic analysis of large Toeplitz determinants. As a byproduct, we obtain a new proof of Okounkov's formula for the (determinantal) correlation functions of the Schur measures on partitions.

Original language	English (US)
Article number	S07
Pages (from-to)	8895-8903
Number of pages	9
Journal	Journal of Physics A: Mathematical and General
Volume	39
Issue number	28
DOIs	https://doi.org/10.1088/0305-4470/39/28/S07
State	Published - Jul 14 2006

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)

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10.1088/0305-4470/39/28/S07

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abstract = "We prove a conjecture of Widom (2002 Int. Math. Res. Not. 455-64 (Preprint math/0108008)) about the reality of eigenvalues of certain infinite matrices arising in asymptotic analysis of large Toeplitz determinants. As a byproduct, we obtain a new proof of Okounkov's formula for the (determinantal) correlation functions of the Schur measures on partitions.",

author = "Alexei Borodin and Alexei Novikov",

note = "Funding Information: The authors thank S. Kalmykov and B. Nagy for bringing the paper [14] to their attention. The first author was supported by the European Research Council , Advanced Grant No. 267055 . The second author was supported by the Austrian Science Fund , project no: P22025-N18 . ",

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On a conjecture of Widom

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