TY - JOUR
T1 - Universality for orthogonal and symplectic Laguerre-type ensembles
AU - Deift, P.
AU - Gioev, D.
AU - Kriecherbauer, T.
AU - Vanlessen, M.
N1 - Funding Information:
The work of the first author was supported in part by the NSF grant DMS– 0500923. While this work was being completed, the first 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.
Funding Information:
The work of the second author was supported in part by the NSF grant DMS– 0556049. The second author would like to thank the Courant Institute and Caltech for hospitality.
PY - 2007/10
Y1 - 2007/10
N2 - We give a proof of the Universality Conjecture for orthogonal (β=1) and symplectic (β=4) random matrix ensembles of Laguerre-type in the bulk of the spectrum as well as at the hard and soft spectral edges. Our results are stated precisely in the Introduction (Theorems 1.1, 1.4, 1.6 and Corollaries 1.2, 1.5, 1.7). They concern the appropriately rescaled kernels K n, β, correlation and cluster functions, gap probabilities and the distributions of the largest and smallest eigenvalues. Corresponding results for unitary (β=2) Laguerre-type ensembles have been proved by the fourth author in Ref. 23. The varying weight case at the hard spectral edge was analyzed in Ref. 13 for β=2: In this paper we do not consider varying weights. Our proof follows closely the work of the first two authors who showed in Refs. 7, 8 analogous results for Hermite-type ensembles. As in Refs. 7, 8 we use the version of the orthogonal polynomial method presented in Refs. 22, 25, to analyze the local eigenvalue statistics. The necessary asymptotic information on the Laguerre-type orthogonal polynomials is taken from Ref. 23.
AB - We give a proof of the Universality Conjecture for orthogonal (β=1) and symplectic (β=4) random matrix ensembles of Laguerre-type in the bulk of the spectrum as well as at the hard and soft spectral edges. Our results are stated precisely in the Introduction (Theorems 1.1, 1.4, 1.6 and Corollaries 1.2, 1.5, 1.7). They concern the appropriately rescaled kernels K n, β, correlation and cluster functions, gap probabilities and the distributions of the largest and smallest eigenvalues. Corresponding results for unitary (β=2) Laguerre-type ensembles have been proved by the fourth author in Ref. 23. The varying weight case at the hard spectral edge was analyzed in Ref. 13 for β=2: In this paper we do not consider varying weights. Our proof follows closely the work of the first two authors who showed in Refs. 7, 8 analogous results for Hermite-type ensembles. As in Refs. 7, 8 we use the version of the orthogonal polynomial method presented in Refs. 22, 25, to analyze the local eigenvalue statistics. The necessary asymptotic information on the Laguerre-type orthogonal polynomials is taken from Ref. 23.
KW - Bulk
KW - Hard edge
KW - Laguerre-type weights
KW - Orthogonal and symplectic ensembles
KW - Random matrix theory
KW - Soft edge
KW - Universality
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U2 - 10.1007/s10955-007-9325-x
DO - 10.1007/s10955-007-9325-x
M3 - Article
AN - SCOPUS:36448967422
SN - 0022-4715
VL - 129
SP - 949
EP - 1053
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 5-6
ER -