 Restriction exponent of a chordal filling

A conformally invariant random chordal filling has exponent $\alpha$ when its avoidance probability for every admissible hull $A$ is the displayed power, where ${\Phi }_A$ fixes zero and has derivative one at infinity. Composition of two hull-removing maps and the chain rule make conditional image avoidance probabilities the same as unconditional ones. The avoidance probabilities determine a chordal filling law principle therefore implies the chordal restriction property. Independent unions followed by filling add exponents, since avoidance probabilities multiply.