On the proof of Universality for orthogonal and symplectic ensembles in random matrix theory

Ovidiu Costin; Percy Deift; Dimitri Gioev

doi:10.1007/s10955-007-9277-1

On the proof of Universality for orthogonal and symplectic ensembles in random matrix theory

Ovidiu Costin, Percy Deift, Dimitri Gioev

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We give a streamlined proof of a quantitative version of a result from P. Deift and D. Gioev, Universality in Random Matrix Theory for Orthogonal and Symplectic Ensembles. IMRP Int. Math. Res. Pap. (in press) which is crucial for the proof of universality in the bulk P. Deift and D. Gioev, Universality in Random Matrix Theory for Orthogonal and Symplectic Ensembles. IMRP Int. Math. Res. Pap. (in press) and also at the edge P. Deift and D. Gioev, {Universality at the edge of the spectrum for unitary, orthogonal and symplectic ensembles of random matrices. Comm. Pure Appl. Math. (in press) for orthogonal and symplectic ensembles of random matrices. As a byproduct, this result gives asymptotic information on a certain ratio of the β=1,2,4 partition functions for log gases.

Original language	English (US)
Pages (from-to)	937-948
Number of pages	12
Journal	Journal of Statistical Physics
Volume	129
Issue number	5-6
DOIs	https://doi.org/10.1007/s10955-007-9277-1
State	Published - Oct 2007

Keywords

Log gases
Orthogonal and symplectic ensembles
Partition function
Random matrix theory
Universality

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-007-9277-1

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title = "On the proof of Universality for orthogonal and symplectic ensembles in random matrix theory",

abstract = "We give a streamlined proof of a quantitative version of a result from P. Deift and D. Gioev, Universality in Random Matrix Theory for Orthogonal and Symplectic Ensembles. IMRP Int. Math. Res. Pap. (in press) which is crucial for the proof of universality in the bulk P. Deift and D. Gioev, Universality in Random Matrix Theory for Orthogonal and Symplectic Ensembles. IMRP Int. Math. Res. Pap. (in press) and also at the edge P. Deift and D. Gioev, {Universality at the edge of the spectrum for unitary, orthogonal and symplectic ensembles of random matrices. Comm. Pure Appl. Math. (in press) for orthogonal and symplectic ensembles of random matrices. As a byproduct, this result gives asymptotic information on a certain ratio of the β=1,2,4 partition functions for log gases.",

keywords = "Log gases, Orthogonal and symplectic ensembles, Partition function, Random matrix theory, Universality",

author = "Ovidiu Costin and Percy Deift and Dimitri Gioev",

note = "Funding Information: The authors would like to thank Thomas Kriecherbauer for useful conversations. The work of the first author was supported in part by NSF grants DMS-0103807 and DMS-0100495. The work of the second author was supported in part by NSF grants DMS-0296084 and DMS-0500923. While this work was being completed, the second author was a Taussky–Todd and Moore Distinguished Scholar at Caltech, and he thanks Professor Tombrello for his sponsorship and Professor Flach for his hospitality. The work of the third author was supported in part by the NSF grant DMS–0556049. The third author would like to thank the Courant Institute and Caltech for hospitality and financial support. Finally, the third author would like to thank the Swedish foundation STINT for providing basic support to visit Caltech.",

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N2 - We give a streamlined proof of a quantitative version of a result from P. Deift and D. Gioev, Universality in Random Matrix Theory for Orthogonal and Symplectic Ensembles. IMRP Int. Math. Res. Pap. (in press) which is crucial for the proof of universality in the bulk P. Deift and D. Gioev, Universality in Random Matrix Theory for Orthogonal and Symplectic Ensembles. IMRP Int. Math. Res. Pap. (in press) and also at the edge P. Deift and D. Gioev, {Universality at the edge of the spectrum for unitary, orthogonal and symplectic ensembles of random matrices. Comm. Pure Appl. Math. (in press) for orthogonal and symplectic ensembles of random matrices. As a byproduct, this result gives asymptotic information on a certain ratio of the β=1,2,4 partition functions for log gases.

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On the proof of Universality for orthogonal and symplectic ensembles in random matrix theory

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Keywords

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