Mathematics – Probability
Scientific paper
2004-05-17
Mathematics
Probability
34 pages
Scientific paper
We construct a measure valued Markov process which we call infinite canonical super-Brownian motion, and which corresponds to the canonical measure of super-Brownian motion conditioned on non-extinction. Infinite canonical super-Brownian motion is a natural candidate for the scaling limit of various random branching objects on $\Z^d$ when these objects are (a) critical; (b) mean-field and (c) infinite. We prove that ICSBM is the scaling limit of the spread-out oriented percolation incipient infinite cluster above 4 dimensions and of incipient infinite branching random walk in any dimension. We conjecture that it also arises as the scaling limit in various other models above the upper-critical dimension, such as the incipient infinite lattice tree above 8 dimensions, the incipient infinite cluster for unoriented percolation, uniform spanning trees above 4 dimensions, and invasion percolation above 6 dimensions. This paper also serves as a survey of recent results linking super-Brownian to scaling limits in statistical mechanics.
No associations
LandOfFree
Infinite canonical super-Brownian motion and scaling limits does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Infinite canonical super-Brownian motion and scaling limits, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Infinite canonical super-Brownian motion and scaling limits will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-284914