Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.00371 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We define and study a natural category of graph limits. The objects are pairs $(π,μ)$, where $π$ (the distribution of vertices) is an abstract probability measure on some abstract measurable space $(X,\mathcal{A})$ and $μ$ (the distribution of edges) is an abstract finite measure on the square $(X,\mathcal{A})^2$. Morphisms are random maps between the underlying measurable spaces which preserve the distribution of vertices as well as the distribution of edges. We also define a convergence notion (inspired by s-convergence) for sequences of graph limits. We apply tools from category theory to prove the compactness of the space of all graph limits.