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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.06020 |
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| _version_ | 1866912183048208384 |
|---|---|
| author | Derrien, Jean-Marc |
| author_facet | Derrien, Jean-Marc |
| contents | The gaussian free field on the unit disk $D$ can be seen as a two-dimensional version of the Brownian bridge on the interval [0,1]. It is intrinsically associated with the Sobolev space $H_0^1 (D)$. To define the latter, we can choose any metric conformally equivalent to the Euclidean metric on $D$. This note is an introduction to the gaussian free field on the unit disk whose aim is to highlight some of the conveniences offered by hyperbolic geometryon $D$ to describe the first properties of this probabilistic object. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06020 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Averaging over the circles the gaussian free field in the Poincar{é} disk Derrien, Jean-Marc Probability The gaussian free field on the unit disk $D$ can be seen as a two-dimensional version of the Brownian bridge on the interval [0,1]. It is intrinsically associated with the Sobolev space $H_0^1 (D)$. To define the latter, we can choose any metric conformally equivalent to the Euclidean metric on $D$. This note is an introduction to the gaussian free field on the unit disk whose aim is to highlight some of the conveniences offered by hyperbolic geometryon $D$ to describe the first properties of this probabilistic object. |
| title | Averaging over the circles the gaussian free field in the Poincar{é} disk |
| topic | Probability |
| url | https://arxiv.org/abs/2501.06020 |