Weak convergence of measure-valued processes and r-point functions

• 成果类型: Article
• 署名作者: Holmes, Mark; Perkins, Edwin
• 署名单位: Euratom; University of British Columbia
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000001088
• 发表日期: 2007
• 页码: 1769-1782
• 关键词: dimensions

摘要

We prove a sufficient set of conditions for a sequence of finite measures on the space of cadlag measure-valued paths to converge to the canonical measure of super-Brownian motion in the sense of convergence of finite-dimensional distributions. The conditions are convergence of the Fourier transform of the r-point functions and perhaps convergence of the survival probabilities. These conditions have recently been shown to hold for a variety of statistical mechanical models, including critical oriented percolation, the critical contact process and lattice trees at criticality, all above their respective critical dimensions.