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• W2952698554 abstract "We consider the critical spread-out contact process in $Zd$ with $dgeq 1$, whose infection range is denoted by $Lgeq1$. The two-point function $tau_t(x)$ is the probability that $xinZd$ is infected at time $t$ by the infected individual located at the origin $oinZd$ at time 0. We prove Gaussian behavior for the two-point function with $Lgeq L_0$ for some finite $L_0=L_0(d)$ for $d>4$. When $dleq 4$, we also perform a local mean-field limit to obtain Gaussian behaviour for $tau_{tT}$ with $t>0$ fixed and $Tto infty$ when the infection range depends on $T$ such that $L_T=LT^b$ for any $b>(4-d)/2d$. The proof is based on the lace expansion and an adaptation of the inductive approach applied to the discretized contact process. We prove the existence of several critical exponents and show that they take on mean-field values. The results in this paper provide crucial ingredients to prove convergence of the finite-dimensional distributions for the contact process towards the canonical measure of super-Brownian motion, which we defer to a sequel of this paper." @default.
• W2952698554 created "2019-06-27" @default.
• W2952698554 creator A5034587660 @default.
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• W2952698554 date "2004-02-04" @default.
• W2952698554 modified "2023-09-27" @default.
• W2952698554 title "Gaussian scaling for the critical spread-out contact process above the upper critical dimension" @default.
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