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Classification of commutation relation for multi-radial SLE — arXiv:2609.19739

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.19739
License (as archived): CC0-1.0
Archived: 2026-10-10T04:23:47.193Z
SHA-256 of the archived text: aeaa8a8e442fe7c3b07a0a405711ac415956bafac47399638709d16fbe60d24e
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How to cite

Classification of commutation relation for multi-radial SLE — arXiv:2609.19739 — arXiv (en), https://arxiv.org/abs/2609.19739 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bc30cf4752ca (Metraipolis archive dc_bc30cf4752ca, sha256 aeaa8a8e442fe7c3b07a0a405711ac415956bafac47399638709d16fbe60d24e)

BibTeX

@misc{dcbc30cf4752ca,
  title = {Classification of commutation relation for multi-radial SLE — arXiv:2609.19739},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.19739},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bc30cf4752ca; sha256 aeaa8a8e442fe7c3b07a0a405711ac415956bafac47399638709d16fbe60d24e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.19739. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Locally commuting multiple radial Schramm-Loewner evolutions ($\mathrm{SLE}_{\kappa}$) are encoded by partition functions satisfying the radial Belavin-Polyakov-Zamolodchikov (BPZ) equations and a conformal Ward identity with spectral parameters $\lambda,\nu\in\mathbb{R}$. For $\kappa>0$ and $\lambda\in\mathbb{R}$, we show that the solution space of the radial BPZ system has dimension $2^n$, where $n$ is the number of variables. We then determine all admissible Ward parameters $\nu$ and the exact dimensions of the subspaces selected by the conformal Ward identity, covering both generic and degenerate cases. The classification reveals a parity difference: nonzero rotation-invariant solutions exist for every $\lambda$ when $n$ is even, but only at finitely many exceptional values when $n$ is odd. When $0<\kappa\leq4$, $\lambda>0$ for odd $n$ or $\lambda>-3/2$ for even $n$, we construct a basis of positive solutions using multiple SLE, providing global realizations of the locally commuting SLEs. At $\kappa=4$, we identify a family of explicit solutions as partition functions for level lines of a Gaussian free field with suitable boundary data and interior singularities.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-18 in math.PR).
Categorie arXiv: Probability (math.PR) ; Mathematical Physics (math-ph); Analysis of PDEs (math.AP).
Pagina del lavoro: https://arxiv.org/abs/2609.19739 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-10T04:09:58.342Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).