Stochastic conformal flows in even dimensions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911733910601728 |
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| author | Piazza, Jack |
| author_facet | Piazza, Jack |
| contents | We define two stochastic analogs of a geometric flow on even-dimensional manifolds called $Q$-curvature flow, and use the theory of Dirichlet forms to construct weak solutions to both. The first of these flows, which we call the normalized $Q$ flow (NQF), preserves the intrinsic volume normalization from the deterministic setting. The second, which we call the Liouville $Q$ flow (LQF), has a different normalization motivated by a similar flow studied in arXiv:1904.10909. The volume dynamics of NQF and LQF are shown to evolve as square Bessel and CIR processes, respectively. We also show that under certain additional conditions, LQF is a stochastic quantization of the even-dimensional Polyakov-Liouville measures recently defined in arXiv:2105.13925. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01217 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic conformal flows in even dimensions Piazza, Jack Probability We define two stochastic analogs of a geometric flow on even-dimensional manifolds called $Q$-curvature flow, and use the theory of Dirichlet forms to construct weak solutions to both. The first of these flows, which we call the normalized $Q$ flow (NQF), preserves the intrinsic volume normalization from the deterministic setting. The second, which we call the Liouville $Q$ flow (LQF), has a different normalization motivated by a similar flow studied in arXiv:1904.10909. The volume dynamics of NQF and LQF are shown to evolve as square Bessel and CIR processes, respectively. We also show that under certain additional conditions, LQF is a stochastic quantization of the even-dimensional Polyakov-Liouville measures recently defined in arXiv:2105.13925. |
| title | Stochastic conformal flows in even dimensions |
| topic | Probability |
| url | https://arxiv.org/abs/2506.01217 |