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
N1 - 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.
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
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U2 - 10.1007/s10955-007-9277-1
DO - 10.1007/s10955-007-9277-1
M3 - Article
AN - SCOPUS:36448983158
SN - 0022-4715
VL - 129
SP - 937
EP - 948
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 5-6
ER -