2023/12/18 by Camia, Federico
#60J67 #81T27 #82B27. Secondary: 82B31 #82B43 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 60K35 #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2312.11047
We prove a formula, first obtained by Kleban, Simmons and Ziff using conformal field theory methods, for the (renormalized) density of a critical percolation cluster in the upper half-plane "anchored" to a point on the real line. The proof is inspired by the method of images. We also show that more general bulk-boundary connection probabilities have well-defined, scale-covariant scaling limits, and prove a formula for the scaling limit of the (renormalized) density of the critical percolation gasket in any domain conformally equivalent to the unit disk.