Radial BPZ equations and partition functions of FK-Ising interfaces conditional on one-arm event

Abstract

Radial BPZ equations come naturally when one solves Dub\'edat's commutation relation in the radial setting. We construct positive solutions to radial BPZ equations and show that partition functions of FK-Ising interfaces in a polygon conditional on a one-arm event are positive solutions to radial BPZ equations.

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