Onsager--Machlup functional for multiple SLEs

Abstract

Recently, Carfagnini and Wang established that the loop Loewner energy can be interpreted as the Onsager--Machlup functional for the SLE loop measure. In this paper, we first interpret the multi-chordal Loewner potential as an Onsager--Machlup functional for the multi-chordal SLE. Subsequently, we extend the conformal deformation formula to the multi-radial Loewner potential and derive the Onsager--Machlup functional for the multi-radial SLE.