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2019 Spatial moments for high-dimensional critical contact process, oriented percolation and lattice trees
Akira Sakai, Gordon Slade
Electron. J. Probab. 24: 1-18 (2019). DOI: 10.1214/19-EJP327

Abstract

Recently, Holmes and Perkins identified conditions which ensure that for a class of critical lattice models the scaling limit of the range is the range of super-Brownian motion. One of their conditions is an estimate on a spatial moment of order higher than four, which they verified for the sixth moment for spread-out lattice trees in dimensions $d>8$. Chen and Sakai have proved the required moment estimate for spread-out critical oriented percolation in dimensions $d+1>4+1$. We use the lace expansion to prove estimates on all moments for the spread-out critical contact process in dimensions $d>4$, which in particular fulfills the spatial moment condition of Holmes and Perkins. Our method of proof is relatively simple, and, as we show, it applies also to oriented percolation and lattice trees. Via the convergence results of Holmes and Perkins, the upper bounds on the spatial moments can in fact be promoted to asymptotic formulas with explicit constants.

Citation

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Akira Sakai. Gordon Slade. "Spatial moments for high-dimensional critical contact process, oriented percolation and lattice trees." Electron. J. Probab. 24 1 - 18, 2019. https://doi.org/10.1214/19-EJP327

Information

Received: 9 October 2018; Accepted: 26 May 2019; Published: 2019
First available in Project Euclid: 22 June 2019

zbMATH: 07089003
MathSciNet: MR3978215
Digital Object Identifier: 10.1214/19-EJP327

Subjects:
Primary: 60K35, 82B27, 82B41

JOURNAL ARTICLE
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