A method of integration over matrix variables: IV

G. Mahoux; M.L. Mehta

doi:doi:10.1051/jp1:1991193

Issue		J. Phys. I France Volume 1, Number 8, August 1991


Page(s)		1093 - 1108
DOI		https://doi.org/10.1051/jp1:1991193

DOI: 10.1051/jp1:1991193
J. Phys. I France 1 (1991) 1093-1108

A method of integration over matrix variables: IV

G. Mahoux and M.L. Mehta

S.Ph.T., C.E.N. Saclay, 91191 Gif-sur-Yvette Cedex, France

(Received 1 February 1991, revised 7 April 1991, accepted 12 April 1991)

Abstract
The m-point correlation function

$\begin{displaymath}\int \left [\prod_{i=1}^n \mu (x_i)\right]\left[\prod_{1\le j... ...}\vert x_j-x_k\vert^{\beta}\right] {\rm d}x_{m+1}...{\rm d}x_n,\end{displaymath}$

is calculated for the three values $\beta=1,2$ and 4, and integers m and n with $0\le m\le n$ . For some applications one needs this integral when $\mu(x)=\exp [-V(x)]$ , V(x) an even polynomial, specially in the limit $n\to \infty$ keeping m finite. A conjecture for this limit in the case $\beta=2$ is given when $V(x)=x^2+\gamma x^4$ .