Component sizes of rank-2 multiplicative random graphs
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916434889670656 |
|---|---|
| author | Clancy Jr, David |
| author_facet | Clancy Jr, David |
| contents | We show that in three different critical regimes, the masses of the connected components of rank-2 multiplicative random graph converge to lengths of excursions of a thinned Lévy process, perhaps with random coefficients. The three critical regimes are those identified by Bollobás, Janson and Riordan (2007), the interacting regime identified by Konarovskyi and Limic (2021), and what we call the nearly bipartite regime which has recently gained interest for its connection to random intersection graphs. Our results are able to extend some of the results by Baslingker et al. (2023) on component sizes of the stochastic blockmodel with two types and those of Federico (2019) and Wang (2023) on the sizes of the connected components of random intersection graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09224 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Component sizes of rank-2 multiplicative random graphs Clancy Jr, David Probability 05C80 We show that in three different critical regimes, the masses of the connected components of rank-2 multiplicative random graph converge to lengths of excursions of a thinned Lévy process, perhaps with random coefficients. The three critical regimes are those identified by Bollobás, Janson and Riordan (2007), the interacting regime identified by Konarovskyi and Limic (2021), and what we call the nearly bipartite regime which has recently gained interest for its connection to random intersection graphs. Our results are able to extend some of the results by Baslingker et al. (2023) on component sizes of the stochastic blockmodel with two types and those of Federico (2019) and Wang (2023) on the sizes of the connected components of random intersection graphs. |
| title | Component sizes of rank-2 multiplicative random graphs |
| topic | Probability 05C80 |
| url | https://arxiv.org/abs/2410.09224 |