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• W2949325468 abstract "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." @default.
• W2949325468 created "2019-06-27" @default.
• W2949325468 creator A5034587660 @default.
• W2949325468 date "2004-05-17" @default.
• W2949325468 modified "2023-09-27" @default.
• W2949325468 title "Infinite canonical super-Brownian motion and scaling limits" @default.
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• W2949325468 hasPublicationYear "2004" @default.
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