Geodesic
Limit correlation functions at zero for fixed trace random matrix ensembles
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 68-80 
F. Götze; M. I. Gordin; A. Levina. Limit correlation functions at zero for fixed trace random matrix ensembles. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 68-80. http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a3/
@article{ZNSL_2007_341_a3,
     author = {F. G\"otze and M. I. Gordin and A. Levina},
     title = {Limit correlation functions at zero for fixed trace random matrix ensembles},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {68--80},
     year = {2007},
     volume = {341},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a3/}
}
TY  - JOUR
AU  - F. Götze
AU  - M. I. Gordin
AU  - A. Levina
TI  - Limit correlation functions at zero for fixed trace random matrix ensembles
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2007
SP  - 68
EP  - 80
VL  - 341
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a3/
LA  - ru
ID  - ZNSL_2007_341_a3
ER  - 
%0 Journal Article
%A F. Götze
%A M. I. Gordin
%A A. Levina
%T Limit correlation functions at zero for fixed trace random matrix ensembles
%J Zapiski Nauchnykh Seminarov POMI
%D 2007
%P 68-80
%V 341
%U http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a3/
%G ru
%F ZNSL_2007_341_a3

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The large-$N$ limit of the eigenvalue correlation functions is examined in a neighborhood of zero for the spectra of $N\times N-$Hermitian matrices chosen at random from the Hilbert–Schmidt sphere of appropriate radius. Dyson's famous $\sin\pi(t_1-t_2)/\pi(t_1-t_2)$-kernel asymptotics is extended to this class of random matrix ensembles.

[1] G. Akemann, G. M. Cicuta, L. Molinari, and G. Vernizzi, “Compact support probability distributions in random matrix theory”, Phys. Rev. E (3), 59:2 (1999), 489–1497, part A | DOI | MR

[2] G. Akemann and G. Vernizzi, “Macroscopic and microscopic (non-)universality of compact support random matrix theory”, Nuclear Phys. B, 583:3 (2000), 739–757 | DOI | MR | Zbl

[3] F. Götze and M. Gordin, Limit correlation functions for Hilbert–Schmidt random matrix ensembles, University of Bielefeld. SFB 701. Preprint No 06-042, 2006

[4] K. Johansson, “Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices”, Comm. Math. Phys., 215:3 (2001), 683–705 | DOI | MR | Zbl

[5] M. L. Mehta, Random matrices, Academic Press Inc., Boston, MA, 1991 | MR | Zbl

[6] V. V. Petrov, Summy nezavisimykh sluchainykh velichin, Nauka, M., 1972 | MR

[7] N. Rosenzweig, “Statistical mechanics of equally likely quantum systems”, Statistical Physics (Brandeis Summer Institute, 1962, Vol. 3), W. A. Benjamin, NY, 1963, 91–158 | MR

[8] A. B. Soshnikov, “Determinantnye tochechnye sluchainye polya”, Uspekhi mat. nauk, 55:5(335) (2000), 107–160 | MR | Zbl

[9] C. A. Tracy and H. Widom, “Correlation functions, cluster functions, and spacing distributions for random matrices”, J. Statist. Phys., 92:5–6 (1998), 809–835 | DOI | MR | Zbl