## The Annals of Probability

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

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 35, Number 5 (2007), 1769-1782.

Dates
First available in Project Euclid: 5 September 2007

https://projecteuclid.org/euclid.aop/1189000927

Digital Object Identifier
doi:10.1214/009117906000001088

Mathematical Reviews number (MathSciNet)
MR2349574

Zentralblatt MATH identifier
1124.60046

#### Citation

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

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