| Numéro |
J. Phys. I France
Volume 3, Numéro 3, March 1993
|
|
|---|---|---|
| Page(s) | 697 - 715 | |
| DOI | https://doi.org/10.1051/jp1:1993100 | |
DOI: 10.1051/jp1:1993100
J. Phys. I France 3 (1993) 697-715
S.Ph.T., C.E. Saclay, F-91191 Gif-sur-Yvette Cedex, France
2.30 - 2.90 - 5.90
© Les Editions de Physique 1993
J. Phys. I France 3 (1993) 697-715
Level spacing functions and non linear differential equations
G. Mahoux and M.L. MehtaS.Ph.T., C.E. Saclay, F-91191 Gif-sur-Yvette Cedex, France
Abstract
The Fredholm determinant of the kernel sin
on the finite interval
(-t, t), appears in the theory of random matrices and in some other problems of mathematical physics. In a previous article we studied
the functions
S(t),
A(t) and
B(t) related to this Fredholm determinant, and derived relations among and differential equations for them. Here we exploit these
relations to deduce the power series at
t = 0, and the asymptotic behaviour at
, of the various level spacing functions of the random matrix theory.
2.30 - 2.90 - 5.90
© Les Editions de Physique 1993