Factorization formulas for 2D critical percolation, revisited

R.P. Conijn

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)4102-4116
JournalStochastic Processes and Their Applications
Volume125
Issue number11
DOIs
Publication statusPublished - 2015

Bibliographical note

PT: J; NR: 15; TC: 0; J9: STOCH PROC APPL; PG: 15; GA: CR3TJ; UT: WOS:000361255700004

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