Stochastic Komatu–Loewner evolutions and BMD domain constant

Abstract

For Komatu–Loewner equation on a standard slit domain, we randomize the Jordan arc in a manner similar to that of Schramm (2000) to find the SDEs satisfied by the induced motion ξ(t) on ∂H and the slit motion s(t). The diffusion coefficient α and drift coefficient b of such SDEs are homogeneous functions.Next with solutions of such SDEs, we study the corresponding stochastic Komatu–Loewner evolution, denoted as SKLEα,b. We introduce a function bBMD measuring the discrepancy of a standard slit domain from H relative to BMD. We show that SKLE6,−bBMD enjoys a locality property.