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Lattice trees, percolation and super-Brownian motion

Gordon Slade
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Abstract

This paper surveys the results of recent collaborations with Eric Derbez and with Takashi Hara, which show that intergrated super-Brownian excursion (ISE) arises as the scaling limit of both lattice trees and the incipient infinite percolation cluster, in high dimensions. A potential extension to oriented percolation is also mentioned.

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Gordon Slade. 1999-05-11. Lattice trees, percolation and super-Brownian motion. https://arxiv.org/abs/math/9905200

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