On a conjecture of Widom
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.
Copyright © Institute of Physics and IOP Publishing Limited 2006. Received 9 September 2005, in final form 14 November 2005. Published 27 June 2006. Print publication: Issue 28 (14 July 2006). One of the authors (AB) was partially supported by the NSF grant DMS-0402047.