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Mean-Field Behavior for the Survival Probability and the Percolation Point-to-Surface Connectivity

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Abstract

We consider the critical survival probability (up to timet) for oriented percolation and the contact process, and the point-to-surface (of the ball of radiust) connectivity for critical percolation. Let θt denote both quantities. We prove in a unified fashion that, if θt exhibits a power law and both the two-point function and its certain restricted version exhibit the same mean-field behavior, then θt=t-1 for the time-oriented models with d > 4 and θt=t-2 for percolation with d > 7.

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  1. EURANDOM, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Akira Sakai

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  1. Akira Sakai
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Sakai, A. Mean-Field Behavior for the Survival Probability and the Percolation Point-to-Surface Connectivity. Journal of Statistical Physics 117, 111–130 (2004). https://doi.org/10.1023/B:JOSS.0000044061.83860.62

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  • DOI: https://doi.org/10.1023/B:JOSS.0000044061.83860.62

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