Onsager--Machlup functional for multiple SLEs

TL;DR

This paper extends the Onsager--Machlup functional interpretation to multi-chordal and multi-radial SLEs, providing new insights into their probabilistic and conformal properties.

Contribution

It introduces the Onsager--Machlup functional for multi-chordal and multi-radial SLEs, expanding the theoretical framework for these stochastic processes.

Findings

Multi-chordal Loewner potential as Onsager--Machlup functional

Conformal deformation formula extended to multi-radial Loewner potential

Derived Onsager--Machlup functional for multi-radial SLE

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.