SLE_k: correlation functions in the coefficient problem

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.

References in corpus (1)

• Stochastic geometry of critical curves, Schramm-Loewner evolutions, and conformal field theory

Cited by in corpus (5)

• On Harmonic Measure of the Whole Plane Levy-Loewner Evolution
• On Exact Multi-fractal Spectrum of the Whole-Plane SLE
• Integral means spectrum of whole-plane SLE
• On Integrability and Exact Solvability in Deterministic and Stochastic Laplacian Growth
• Stochastic Loewner Evolutions, Fuchsian Systems and Orthogonal Polynomials