TY - JOUR
T1 - Factorization formulas for 2D critical percolation, revisited
AU - Conijn, R.P.
N1 - PT: J; NR: 15; TC: 0; J9: STOCH PROC APPL; PG: 15; GA: CR3TJ; UT: WOS:000361255700004
PY - 2015
Y1 - 2015
N2 - We consider critical site percolation on the triangular lattice in the upper half-plane. Let u1,u2 be two sites on the boundary and w a site in the interior. It was predicted by Simmons et al. (2007) that the ratio P(nu1虠nu2虠nw)2/P(nu1虠nu2).P(nu1虠nw).P(nu2虠nw) converges to KF as n→8, where x虠y denotes that x and y are in the same cluster, and KF is a constant. Beliaev and Izyurov (2012) proved an analog of this in the scaling limit. We prove, using their result and a generalized coupling argument, the earlier mentioned prediction. Furthermore we prove a factorization formula for P(nu2虠[nu1,nu1+s];nw虠[nu1,nu1+s]), where s>0.
AB - We consider critical site percolation on the triangular lattice in the upper half-plane. Let u1,u2 be two sites on the boundary and w a site in the interior. It was predicted by Simmons et al. (2007) that the ratio P(nu1虠nu2虠nw)2/P(nu1虠nu2).P(nu1虠nw).P(nu2虠nw) converges to KF as n→8, where x虠y denotes that x and y are in the same cluster, and KF is a constant. Beliaev and Izyurov (2012) proved an analog of this in the scaling limit. We prove, using their result and a generalized coupling argument, the earlier mentioned prediction. Furthermore we prove a factorization formula for P(nu2虠[nu1,nu1+s];nw虠[nu1,nu1+s]), where s>0.
U2 - 10.1016/j.spa.2015.05.017
DO - 10.1016/j.spa.2015.05.017
M3 - Article
SN - 0304-4149
VL - 125
SP - 4102
EP - 4116
JO - Stochastic Processes and Their Applications
JF - Stochastic Processes and Their Applications
IS - 11
ER -