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Spatial moments for high-dimensional critical contact process, oriented percolation and lattice trees
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| Title: | Spatial moments for high-dimensional critical contact process, oriented percolation and lattice trees |
| Authors: | Sakai, Akira Browse this author →KAKEN DB | | Slade, Gordon Browse this author |
| Keywords: | contact process | | oriented percolation | | lattice trees | | lace expansion |
| Issue Date: | 7-Aug-2019 |
| Publisher: | University of Washington |
| Journal Title: | Electronic journal of probability |
| Volume: | 24 |
| Start Page: | 65 |
| Publisher 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. |
| Rights: | https://creativecommons.org/licenses/by/4.0/ |
| Type: | article |
| URI: | http://hdl.handle.net/2115/75169 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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