Point Processes with Specified Low Order Correlations

E. Caglioti, T. Kuna, J.L. Lebowitz, E.R. Speer

2006, v.12, Issue 2, 257-272

ABSTRACT

Given functions $\rho_k({\ r}_1,{\ldots},{\ r}_k)$, defined on $(R^d)^k$ or $(Z^d)^k$ for $k = 1,{\ldots},n$, we wish to determine whether they are the first $n$ correlation functions of some point process in $R^d$ or $Z^d$, respectively, and if so what we can say about the process. We give partial answers to these questions and discuss some examples.

Keywords: point processes,realizability,maximum entropy,Gibbs measures