NECESSARY AND SUFFICIENT CONDITIONS FOR REALIZABILITY OF POINT PROCESSES

• 成果类型: Article
• 署名作者: Kuna, Tobias; Lebowitz, Joel L.; Speer, Eugene R.
• 署名单位: University of Reading; Rutgers University System; Rutgers University New Brunswick
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP703
• 发表日期: 2011
• 页码: 1253-1281
• 关键词: statistical mechanical systems; density matrices; particles; STATES

摘要

We give necessary and sufficient conditions for a pair of (generalized) functions rho(1)(r(1)) and rho(2) (r(1), r(2)), r(i) is an element of X, to be the density and pair correlations of some point process in a topological space X, for example, R(d), Z(d) or a subset of these. This is an infinite-dimensional version of the classical truncated moment problem. Standard techniques apply in the case in which there can be only a bounded number of points in any compact subset of X. Without this restriction we obtain, for compact X, strengthened conditions which are necessary and sufficient for the existence of a process satisfying a further requirement-the existence of a finite third order moment. We generalize the latter conditions in two distinct ways when X is not compact.