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- W2897546291 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 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." @default.
- W2897546291 created "2018-10-26" @default.
- W2897546291 creator A5007640171 @default.
- W2897546291 creator A5052455821 @default.
- W2897546291 date "2018-10-09" @default.
- W2897546291 modified "2023-09-27" @default.
- W2897546291 title "Spatial moments for high-dimensional critical contact process, oriented percolation and lattice trees" @default.
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- W2897546291 doi "https://doi.org/10.48550/arxiv.1810.04011" @default.
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