 03371 Remco van der Hofstad and Akira Sakai
 Gaussian scaling for the critical spreadout contact process above the upper critical dimension
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Aug 15, 03

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Abstract. We consider the critical spreadout contact process in the
ddimensional integer lattice \Zd, whose infection range
is denoted by L. The twopoint function \tau_t(x) is the
probability that x \in \Zd is infected at time t by the
infected individual located at the origin at time 0. We
prove Gaussian behavior for the twopoint function with
L \geq L_0 for some finite L_0 = L_0(d) for d > 4.
When d \leq 4, we also perform a local meanfield limit to
obtain Gaussian behaviour for \tau_{tT}(x) with t > 0
fixed and T \to \infty when the infection range depends
on T such that L_T = L T^b for any b > (4d) / 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 meanfield values. The results
in this paper provide crucial ingredients to prove convergence
of the finitedimensional distributions for the contact process
towards the canonical measure of superBrownian motion, which
we defer to a sequel of this paper.
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