TY - JOUR

T1 - Mean-field behavior for the survival probability and the percolation point-to-surface connectivity

AU - Sakai, A.

PY - 2004

Y1 - 2004

N2 - 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 t denote both quantities. We prove in a unified fashion that, if t exhibits a power law and both the two-point function and its certain restricted version exhibit the same mean-field behavior, then t=t-1 for the time-oriented models with d > 4 and t=t-2 for percolation with d > 7.

AB - 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 t denote both quantities. We prove in a unified fashion that, if t exhibits a power law and both the two-point function and its certain restricted version exhibit the same mean-field behavior, then t=t-1 for the time-oriented models with d > 4 and t=t-2 for percolation with d > 7.

U2 - 10.1023/B:JOSS.0000044061.83860.62

DO - 10.1023/B:JOSS.0000044061.83860.62

M3 - Article

VL - 117

SP - 111

EP - 130

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1-2

ER -