Large random intersection graphs inside the critical window and triangle counts
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917963786878976 |
|---|---|
| author | Wang, Minmin |
| author_facet | Wang, Minmin |
| contents | We identify the scaling limit of random intersection graphs inside their critical windows. The limit graphs vary according to the clustering regimes, and coincide with the continuum Erdos--Renyi graph in two out of the three regimes. Our approach to the scaling limit relies upon the close connection of random intersection graphs with binomial bipartite graphs, as well as a graph exploration algorithm on the latter. This further allows us to prove limit theorems for the number of triangles in the large connected components of the graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_13694 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Large random intersection graphs inside the critical window and triangle counts Wang, Minmin Probability We identify the scaling limit of random intersection graphs inside their critical windows. The limit graphs vary according to the clustering regimes, and coincide with the continuum Erdos--Renyi graph in two out of the three regimes. Our approach to the scaling limit relies upon the close connection of random intersection graphs with binomial bipartite graphs, as well as a graph exploration algorithm on the latter. This further allows us to prove limit theorems for the number of triangles in the large connected components of the graphs. |
| title | Large random intersection graphs inside the critical window and triangle counts |
| topic | Probability |
| url | https://arxiv.org/abs/2309.13694 |