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September 2007 Weak convergence of measure-valued processes and r-point functions
Mark Holmes, Edwin Perkins
Ann. Probab. 35(5): 1769-1782 (September 2007). DOI: 10.1214/009117906000001088


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.


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Mark Holmes. Edwin Perkins. "Weak convergence of measure-valued processes and r-point functions." Ann. Probab. 35 (5) 1769 - 1782, September 2007.


Published: September 2007
First available in Project Euclid: 5 September 2007

zbMATH: 1124.60046
MathSciNet: MR2349574
Digital Object Identifier: 10.1214/009117906000001088

Primary: 60G57 , 60K35
Secondary: 60F05

Keywords: canonical measure , critical oriented percolation , Measure-valued processes , r-point functions , Super-Brownian motion

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 5 • September 2007
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