Optimal graphons in the edge-2star model
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911392566607872 |
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| author | Radin, Charles Sadun, Lorenzo |
| author_facet | Radin, Charles Sadun, Lorenzo |
| contents | In the edge-2star model with hard constraints we prove the existence of an open set of constraint parameters, bisected by a line segment on which there are nonunique entropy-optimal graphons related by a symmetry. At each point in the open set but off the line segment there is a unique entropy-optimizer, bipodal and varying analytically with the constraints. We also show that throughout another open set, containing a different portion of the same line of symmetry, there is instead a unique optimal graphon, varying analytically with the parameters. We explore the extent of these open sets, determining the point at which a symmetric graphon ceases to be a local maximizer of the entropy. Finally, we prove some foundational theorems in a general setting, relating optimal graphons to the Boltzmann entropy and the generic structure of large constrained random graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00333 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal graphons in the edge-2star model Radin, Charles Sadun, Lorenzo Probability Mathematical Physics Combinatorics 60xx In the edge-2star model with hard constraints we prove the existence of an open set of constraint parameters, bisected by a line segment on which there are nonunique entropy-optimal graphons related by a symmetry. At each point in the open set but off the line segment there is a unique entropy-optimizer, bipodal and varying analytically with the constraints. We also show that throughout another open set, containing a different portion of the same line of symmetry, there is instead a unique optimal graphon, varying analytically with the parameters. We explore the extent of these open sets, determining the point at which a symmetric graphon ceases to be a local maximizer of the entropy. Finally, we prove some foundational theorems in a general setting, relating optimal graphons to the Boltzmann entropy and the generic structure of large constrained random graphs. |
| title | Optimal graphons in the edge-2star model |
| topic | Probability Mathematical Physics Combinatorics 60xx |
| url | https://arxiv.org/abs/2305.00333 |