SLE_k: correlation functions in the coefficient problem

TL;DR

This paper uses correlation functions to analyze the coefficient problem in stochastic geometry, providing proofs for conjectured patterns and exploring higher moments and multifractal spectra in SLE_kappa.

Contribution

It introduces a correlation function approach to the coefficient problem in SLE_kappa, proving conjectures and proposing methods for higher moments analysis.

Findings

Proof of universal second moment patterns for SLE_kappa coefficients

Proposal of multi-point correlation functions for higher moments

Discussion of the multifractal spectrum of SLE_kappa

Abstract

We apply the method of correlation functions to the coefficient problem in stochastic geometry. In particular, we give a proof for some universal patterns conjectured by M. Zinsmeister for the second moments of the Taylor coefficients for special values of kappa in the whole-plane Schramm-Loewner evolution (SLE_kappa). We propose to use multi-point correlation functions for the study of higher moments in coefficient problem. Generalizations related to the Levy-type processes are also considered. The exact multifractal spectrum of considered version of the whole-plane SLE_kappa is discussed.