Emergence in graphs with near-extreme constraints
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915467043536896 |
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| author | Radin, Charles Sadun, Lorenzo |
| author_facet | Radin, Charles Sadun, Lorenzo |
| contents | We consider entropy-optimal graphons associated with extreme and near-extreme constraints on the densities of edges and triangles. We prove that the optimizers for near-extreme constraints are unique and multipodal and are perturbations of the previously known unique optimzers for extreme constraints. This proves the existence of infinitely many phases. We determine the podal structures in these phases and prove the existence of phase transitions between them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14556 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Emergence in graphs with near-extreme constraints Radin, Charles Sadun, Lorenzo Probability Mathematical Physics Combinatorics 60C05 We consider entropy-optimal graphons associated with extreme and near-extreme constraints on the densities of edges and triangles. We prove that the optimizers for near-extreme constraints are unique and multipodal and are perturbations of the previously known unique optimzers for extreme constraints. This proves the existence of infinitely many phases. We determine the podal structures in these phases and prove the existence of phase transitions between them. |
| title | Emergence in graphs with near-extreme constraints |
| topic | Probability Mathematical Physics Combinatorics 60C05 |
| url | https://arxiv.org/abs/2411.14556 |