The Annals of Probability
- Ann. Probab.
- Volume 35, Number 5 (2007), 1769-1782.
Weak convergence of measure-valued processes and r-point functions
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.
Ann. Probab., Volume 35, Number 5 (2007), 1769-1782.
First available in Project Euclid: 5 September 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G57: Random measures 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60F05: Central limit and other weak theorems
Holmes, Mark; Perkins, Edwin. Weak convergence of measure-valued processes and r -point functions. Ann. Probab. 35 (2007), no. 5, 1769--1782. doi:10.1214/009117906000001088. https://projecteuclid.org/euclid.aop/1189000927