Emergence in graphs with near-extreme constraints

Fuente: arXiv
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Main Authors: Radin, Charles, Sadun, Lorenzo
Format: Preprint
Published: 2024
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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