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 -