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A Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux

Baik, Jinho and Deift, Percy and Rains, Eric (2001) A Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux. Communications in Mathematical Physics, 223 (3). pp. 627-672. ISSN 0010-3616. https://resolver.caltech.edu/CaltechAUTHORS:20171003-074824665

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Abstract

We obtain an identity between Fredholm determinants of two kinds of operators, one acting on functions on the unit circle and the other acting on functions on a subset of the integers. This identity is a generalization of an identity between a Toeplitz determinant and a Fredholm determinant that has appeared in the random permutation context. Using this identity, we prove, in particular, convergence of moments for arbitrary rows of a random Young diagram under Plancherel measure.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s002200100555DOIArticle
https://link.springer.com/article/10.1007%2Fs002200100555PublisherArticle
http://rdcu.be/wqdXPublisherFree ReadCube access
https://arxiv.org/abs/math/0012117arXivDiscussion Paper
Additional Information:© 2001 Springer-Verlag Berlin Heidelberg. Received: 19 December 2000; Accepted: 23 July 2001. The authors would like to thank Xin Zhou for useful comments. The authors would also like to thank Albrecht Böttcher for pointing out a calculational error in an earlier version of the text. The work of the first author was supported in part by NSF Grant # DMS 97-29992. The work of the second author was supported in part by NSF Grant # DMS 00-03268, and also by the Guggenheim Foundation.
Funders:
Funding AgencyGrant Number
NSFDMS 97-29992
NSFDMS 00-03268
John Simon Guggenheim FoundationUNSPECIFIED
Issue or Number:3
Record Number:CaltechAUTHORS:20171003-074824665
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20171003-074824665
Official Citation:Baik, J., Deift, P. & Rains, E. Commun. Math. Phys. (2001) 223: 627. https://doi.org/10.1007/s002200100555
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81981
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:03 Oct 2017 18:02
Last Modified:03 Oct 2019 18:49

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