Back to Search
Start Over
Splitting algorithm and normed convergence for drawing the random fractal Loewner curves
- Publication Year :
- 2021
-
Abstract
- In the first part of the paper we propose and study the approximation of the $SLE_\kappa$ trace via the Ninomiya-Victoir splitting algorithm. We prove the uniform convergence in probability with respect to the sup-norm to the distance between the $SLE_\kappa$ trace and the output of the Ninomiya-Victoir splitting algorithm when applied in the context of the Loewner differential equation. Further investigations on the $L^p$-norm convergence is also exhibited, shedding light on the more delicate convergence structure. In the second part we show the uniform convergence of the approximation of the $SLE_\kappa$ trace obtained using a different scheme that is based on the linear interpolation of the Brownian driving force.<br />Comment: 25 pages, 1 figure; Refining of the text and of the results. Change of the title
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2110.10631
- Document Type :
- Working Paper