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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.04958 |
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| _version_ | 1866914966588620800 |
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| author | Leblé, Thomas |
| author_facet | Leblé, Thomas |
| contents | We prove that, at arbitrary positive temperature, every infinite-volume local limit point of the two-dimensional one-component plasma (2DOCP, also known as Coulomb or log-gas, or jellium) satisfies a system of Dobrushin-Lanford-Ruelle (DLR) equations - in particular, we explain how to rigorously make sense of those despite the long-range interaction. We also show number-rigidity and translation-invariance of the limiting processes. This extends results known for the infinite Ginibre ensemble. The proofs combine recent results on finite 2DOCP's and classical infinite-volume techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04958 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | DLR equations, number-rigidity and translation-invariance for infinite-volume limit points of the 2DOCP Leblé, Thomas Probability We prove that, at arbitrary positive temperature, every infinite-volume local limit point of the two-dimensional one-component plasma (2DOCP, also known as Coulomb or log-gas, or jellium) satisfies a system of Dobrushin-Lanford-Ruelle (DLR) equations - in particular, we explain how to rigorously make sense of those despite the long-range interaction. We also show number-rigidity and translation-invariance of the limiting processes. This extends results known for the infinite Ginibre ensemble. The proofs combine recent results on finite 2DOCP's and classical infinite-volume techniques. |
| title | DLR equations, number-rigidity and translation-invariance for infinite-volume limit points of the 2DOCP |
| topic | Probability |
| url | https://arxiv.org/abs/2410.04958 |