2021-12-07T22:28:28Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000402292021-03-01T21:04:48ZA Limit Formula for a Class of Gibbs Measures with Long Range Pair InteractionsChiyonobu, Taizo138827415application/pdfLet $X_i,\ i=1,2,\dots$ 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.departmental bulletin paperGraduate School of Mathematical Sciences, The University of Tokyo2000application/pdfJournal of mathematical sciences, the University of Tokyo37463486AA1102165313405705https://repository.dl.itc.u-tokyo.ac.jp/record/40229/files/jms070306.pdfeng