A para-controlled approach to the stochastic Yang-Mills equation in two dimensions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916896773767168 |
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| author | Bringmann, Bjoern Cao, Sky |
| author_facet | Bringmann, Bjoern Cao, Sky |
| contents | We consider the stochastic Yang-Mills heat equation on the two-dimensional torus. Using regularity structures, Chandra, Chevyrev, Hairer, and Shen previously proved both the local well-posedness and gauge-covariance of this model. In this article, we revisit their results using para-controlled calculus. One of the main ingredients is a new coordinate-invariant perspective on vector-valued stochastic objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_07197 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A para-controlled approach to the stochastic Yang-Mills equation in two dimensions Bringmann, Bjoern Cao, Sky Probability Mathematical Physics Analysis of PDEs 60H17, 60H15, 35R60, 81T13 We consider the stochastic Yang-Mills heat equation on the two-dimensional torus. Using regularity structures, Chandra, Chevyrev, Hairer, and Shen previously proved both the local well-posedness and gauge-covariance of this model. In this article, we revisit their results using para-controlled calculus. One of the main ingredients is a new coordinate-invariant perspective on vector-valued stochastic objects. |
| title | A para-controlled approach to the stochastic Yang-Mills equation in two dimensions |
| topic | Probability Mathematical Physics Analysis of PDEs 60H17, 60H15, 35R60, 81T13 |
| url | https://arxiv.org/abs/2305.07197 |