Splitting algorithm and normed convergence for drawing the random Loewner curves
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916824520589312 |
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| author | Chen, Jiaming Margarint, Vlad |
| author_facet | Chen, Jiaming Margarint, Vlad |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02776 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Splitting algorithm and normed convergence for drawing the random Loewner curves Chen, Jiaming Margarint, Vlad Probability 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. |
| title | Splitting algorithm and normed convergence for drawing the random Loewner curves |
| topic | Probability |
| url | https://arxiv.org/abs/2507.02776 |