On Convergence to SLE6 II: Discrete Approximations and Extraction of Cardy's Formula for General Domains

Abstract

We show how to extract Cardy's Formula for a general class of domains given the requisite interior analyticity statement. This is accomplished by a careful study of the interplay between discretization schemes and extraction of limiting boundary values. Of particular importance to the companion work (Binder et al. in J. Stat. Phys., 2010) we establish these results for slit domains and for the critical percolation models introduced in Chayes and Lei (Rev. Math. Phys. 19:511-565, 2007). © 2010 The Author(s).