Splitting algorithm and normed convergence for drawing the random Loewner curves

2025/07/03 by Chen, Jiaming, Margarint, Vlad · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2507.02776

Abstract

Recent advances in Schramm-Loewner evolution have driven increasing interest in non-standard Loewner flows. In this work, we propose a novel splitting algorithm to simulate random Loewner curves with rigorous convergence analysis in sup-norm and L^p. The algorithm is further extended to explore fractional SLE, driven by fractional Brownian motion, and noise-reinforced SLE, incorporating the effect on long-term memory. These exploratory and numerical extensions enable theoretical predictions on fractal dimensions and other statistical phenomena, providing new insights into such dynamics and opening directions for future research.

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