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

James Foster; Terry Lyons; Vlad Margarint

doi:10.1007/s10955-022-02979-3

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

James Foster, Terry Lyons, Vlad Margarint

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Citations (SciVal)

26 Downloads (Pure)

Abstract

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.

Original language	English
Article number	18
Journal	Journal of Statistical Physics
Volume	189
Issue number	2
Early online date	3 Sept 2022
DOIs	https://doi.org/10.1007/s10955-022-02979-3
Publication status	Published - 30 Nov 2022

Bibliographical note

Funding Information:
The first author was supported by the Department of Mathematical Sciences at the University of Bath and the DataSig programme under the EPSRC grant S026347/1. The second author was supported by the DataSig programme and Alan Turing Institute under the EPSRC Grant EP/N510129/1. The last author would like to acknowledge the support of ERC (Grant Agreement No.291244 Esig) between 2015–2017 at OMI Institute, EPSRC 1657722 between 2015-2018, Oxford Mathematical Department Grant and the EPSRC Grant EP/M002896/1 between 2018-2019. In addition, VM acknowledges the support of NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.

Keywords

Numerical methods and simulations
Rough path theory
Schramm–Loewner evolutions

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/s10955-022-02979-3

Asymptotic radius of Loewner Equation and SLE simulation
This is a post-peer-review, pre-copyedit version of an article published in Journal of Statistical Physics. The final authenticated version is available online at: https://link.springer.com/article/10.1007/s10955-022-02979-3
Accepted author manuscript, 551 KBLicence: Unspecified

Cite this

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title = "An Asymptotic Radius of Convergence for the Loewner Equation and Simulation of SLE κ Traces via Splitting",

abstract = "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. ",

keywords = "Numerical methods and simulations, Rough path theory, Schramm–Loewner evolutions",

author = "James Foster and Terry Lyons and Vlad Margarint",

note = "Funding Information: The first author was supported by the Department of Mathematical Sciences at the University of Bath and the DataSig programme under the EPSRC grant S026347/1. The second author was supported by the DataSig programme and Alan Turing Institute under the EPSRC Grant EP/N510129/1. The last author would like to acknowledge the support of ERC (Grant Agreement No.291244 Esig) between 2015–2017 at OMI Institute, EPSRC 1657722 between 2015-2018, Oxford Mathematical Department Grant and the EPSRC Grant EP/M002896/1 between 2018-2019. In addition, VM acknowledges the support of NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai. ",

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