### 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 | |

State | Published - Oct 2007 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Journal of Statistical Physics*,

*129*(5-6), 937-948. https://doi.org/10.1007/s10955-007-9277-1

**On the proof of Universality for orthogonal and symplectic ensembles in random matrix theory.** / Costin, Ovidiu; Deift, Percy; Gioev, Dimitri.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 129, no. 5-6, pp. 937-948. https://doi.org/10.1007/s10955-007-9277-1

}

TY - JOUR

T1 - On the proof of Universality for orthogonal and symplectic ensembles in random matrix theory

AU - Costin, Ovidiu

AU - Deift, Percy

AU - Gioev, Dimitri

PY - 2007/10

Y1 - 2007/10

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.

AB - 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.

KW - Log gases

KW - Orthogonal and symplectic ensembles

KW - Partition function

KW - Random matrix theory

KW - Universality

UR - http://www.scopus.com/inward/record.url?scp=36448983158&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36448983158&partnerID=8YFLogxK

U2 - 10.1007/s10955-007-9277-1

DO - 10.1007/s10955-007-9277-1

M3 - Article

VL - 129

SP - 937

EP - 948

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 5-6

ER -