An elementary approach to quantum length of SLE
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911285384314880 |
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| author | Powell, Ellen Sepúlveda, Avelio |
| author_facet | Powell, Ellen Sepúlveda, Avelio |
| contents | We present an elementary proof establishing the equality of the right and left-sided $\sqrtκ$-quantum lengths for an SLE$_κ$ curve, where $κ\in (0,4]$. We achieve this by demonstrating that the$\sqrtκ$-quantum length is equal to the $(\sqrtκ/2)$-Gaussian multiplicative chaos with reference measure given by half the conformal Minkowski content of the curve, multiplied by $2/(4-κ)$ for $κ\in (0,4)$ and by $1$ for $κ=4$. Our proof relies on a novel "one-sided" approximation of the conformal Minkowski content, which is compatible with the conformal change of coordinates formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03902 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An elementary approach to quantum length of SLE Powell, Ellen Sepúlveda, Avelio Probability Mathematical Physics We present an elementary proof establishing the equality of the right and left-sided $\sqrtκ$-quantum lengths for an SLE$_κ$ curve, where $κ\in (0,4]$. We achieve this by demonstrating that the$\sqrtκ$-quantum length is equal to the $(\sqrtκ/2)$-Gaussian multiplicative chaos with reference measure given by half the conformal Minkowski content of the curve, multiplied by $2/(4-κ)$ for $κ\in (0,4)$ and by $1$ for $κ=4$. Our proof relies on a novel "one-sided" approximation of the conformal Minkowski content, which is compatible with the conformal change of coordinates formula. |
| title | An elementary approach to quantum length of SLE |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2403.03902 |