The real layering field of Brownian loop soup and the Gaussian multiplicative chaos
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912669989076992 |
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| author | Maitra, Sayantan |
| author_facet | Maitra, Sayantan |
| contents | We consider the random field defined by the layering numbers of the Brownian loop soup in a bounded simply connected domain in the complex plane. We call this the layering field and show that, after a suitable renormalization, it converges to the subcritical Gaussian multiplicative chaos. The main technique for our proof is the Wiener-Itô chaos expansion. We also calculate the $n$-point functions of the layering field, show their conformal covariance and discuss their behavior near the boundary of the domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22165 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The real layering field of Brownian loop soup and the Gaussian multiplicative chaos Maitra, Sayantan Probability We consider the random field defined by the layering numbers of the Brownian loop soup in a bounded simply connected domain in the complex plane. We call this the layering field and show that, after a suitable renormalization, it converges to the subcritical Gaussian multiplicative chaos. The main technique for our proof is the Wiener-Itô chaos expansion. We also calculate the $n$-point functions of the layering field, show their conformal covariance and discuss their behavior near the boundary of the domain. |
| title | The real layering field of Brownian loop soup and the Gaussian multiplicative chaos |
| topic | Probability |
| url | https://arxiv.org/abs/2510.22165 |