## A Limit Formula for a Class of Gibbs Measures with Long Range Pair Interactions

J. Math. Sci. Univ. Tokyo
Vol. 7 (2000), No. 3, Page 463--486.

Chiyonobu, Taizo
A Limit Formula for a Class of Gibbs Measures with Long Range Pair Interactions
Let $X_i,\ i=1,2,\dots$ be real-valued {\sl i.i.d.} variables with a compactly supported density. Under certain assumptions on $V,$ we give an asymptotic evaluation of $E[\exp(-\half\sum_{i,j=1}^n V(X_i,X_j))]$ up to the factor $(1+o(1)).$ As an application of this result, we prove a limit formula for a class of Gibbs measures with long range pair interactions.