Local limit theorem for joint subgraph counts
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915061423931392 |
|---|---|
| author | Sah, Ashwin Sawhney, Mehtaab Zhu, Daniel G. |
| author_facet | Sah, Ashwin Sawhney, Mehtaab Zhu, Daniel G. |
| contents | Extending a previous result of the first two authors, we prove a local limit theorem for the joint distribution of subgraph counts in the Erdős-Rényi random graph $G(n,p)$. This limit can be described as a nonlinear transformation of a multivariate normal distribution, where the components of the multivariate normal correspond to the graph factors of Janson. As an application, we show a number of results concerning the existence and enumeration of proportional graphs and related concepts, answering various questions of Janson and collaborators in the affirmative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09535 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local limit theorem for joint subgraph counts Sah, Ashwin Sawhney, Mehtaab Zhu, Daniel G. Probability Combinatorics 60F05 (Primary) 05C80, 60C05 (Secondary) Extending a previous result of the first two authors, we prove a local limit theorem for the joint distribution of subgraph counts in the Erdős-Rényi random graph $G(n,p)$. This limit can be described as a nonlinear transformation of a multivariate normal distribution, where the components of the multivariate normal correspond to the graph factors of Janson. As an application, we show a number of results concerning the existence and enumeration of proportional graphs and related concepts, answering various questions of Janson and collaborators in the affirmative. |
| title | Local limit theorem for joint subgraph counts |
| topic | Probability Combinatorics 60F05 (Primary) 05C80, 60C05 (Secondary) |
| url | https://arxiv.org/abs/2412.09535 |