Construction of a Gibbs measure for the zonal Dirac equation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866908772597760000 |
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| author | de Suzzoni, Anne-Sophie Malézé, Cyril |
| author_facet | de Suzzoni, Anne-Sophie Malézé, Cyril |
| contents | We propose a framework to construct Gibbs measures for the Dirac equation. We consider the Dirac equation on the sphere with a "Hartree-type" nonlinearity. We consider a zonal model, that is the analog of a spherically symmetric model but on the sphere. We build a Gibbs measure for this model. With a compactness argument, we prove the existence of a random variable that is a weak solution to the Dirac equation and whose law is the Gibbs measure at all times. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11730 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Construction of a Gibbs measure for the zonal Dirac equation de Suzzoni, Anne-Sophie Malézé, Cyril Analysis of PDEs Probability We propose a framework to construct Gibbs measures for the Dirac equation. We consider the Dirac equation on the sphere with a "Hartree-type" nonlinearity. We consider a zonal model, that is the analog of a spherically symmetric model but on the sphere. We build a Gibbs measure for this model. With a compactness argument, we prove the existence of a random variable that is a weak solution to the Dirac equation and whose law is the Gibbs measure at all times. |
| title | Construction of a Gibbs measure for the zonal Dirac equation |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2601.11730 |