An Asymptotic Radius of Convergence for the Loewner Equation and Simulation of SLE _κ Traces via Splitting

James Foster, Terry Lyons, Vlad Margarint

OAI: oai:purehost.bath.ac.uk:openaire_cris_publications/695b1f0b-7f2c-406a-b4e7-1da66d482e35 • DOI: https://doi.org/10.1007/s10955-022-02979-3

In this paper, we study the convergence of Taylor approximations for the backward SLE maps near the origin. In addition, this result highlights the limitations of using stochastic Taylor methods for approximating SLE _κ traces. Due to the analytically tractable vector fields of the Loewner equation, we will show the Ninomiya–Victoir splitting is particularly well suited for SLE simulation. We believe that this is the first high order numerical method that has been successfully applied to SLE _κ.

Numerical methods and simulations Rough path theory Schramm–Loewner evolutions /dk/atira/pure/subjectarea/asjc/3100/3109 name=Statistical and Nonlinear Physics /dk/atira/pure/subjectarea/asjc/2600/2610 name=Mathematical Physics