The variational principle for a marked Gibbs point process with infinite-range multibody interactions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914154705584128 |
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| author | Jahnel, Benedikt Köppl, Jonas Steenbeck, Yannic Zass, Alexander |
| author_facet | Jahnel, Benedikt Köppl, Jonas Steenbeck, Yannic Zass, Alexander |
| contents | We prove the Gibbs variational principle for the Asakura--Oosawa model in which particles of random size obey a hardcore constraint of non-overlap and are additionally subject to a temperature-dependent area interaction. The particle size is unbounded, leading to infinite-range interactions, and the potential cannot be written as a $k$-body interaction for fixed $k$. As a byproduct, we also prove the existence of infinite-volume Gibbs point processes satisfying the DLR equations. The essential control over the influence of boundary conditions can be established using the geometry of the model and the hard-core constraint. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_17170 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The variational principle for a marked Gibbs point process with infinite-range multibody interactions Jahnel, Benedikt Köppl, Jonas Steenbeck, Yannic Zass, Alexander Probability Mathematical Physics Primary 82C22, Secondary 60K35 We prove the Gibbs variational principle for the Asakura--Oosawa model in which particles of random size obey a hardcore constraint of non-overlap and are additionally subject to a temperature-dependent area interaction. The particle size is unbounded, leading to infinite-range interactions, and the potential cannot be written as a $k$-body interaction for fixed $k$. As a byproduct, we also prove the existence of infinite-volume Gibbs point processes satisfying the DLR equations. The essential control over the influence of boundary conditions can be established using the geometry of the model and the hard-core constraint. |
| title | The variational principle for a marked Gibbs point process with infinite-range multibody interactions |
| topic | Probability Mathematical Physics Primary 82C22, Secondary 60K35 |
| url | https://arxiv.org/abs/2408.17170 |