00-177 Akira Sakai

Mean-field Critical Behavior for Contact Processes (328K, .ps.gz) Apr 9, 00

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Abstract. We prove the triangle condition for the basic contact process in sufficiently high dimensions and for the spatially spread-out contact process in spatial dimension $d > 4$. Combining with the result of Barsky and Wu in 1998, we prove the mean-field critical behavior for these processes. Our results imply that the upper critical dimension for the contact processes is four.

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