Stein's Method for Spatial Random Graphs
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929576912879616 |
|---|---|
| author | Schuhmacher, Dominic Wirth, Leoni Carla |
| author_facet | Schuhmacher, Dominic Wirth, Leoni Carla |
| contents | In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main theorems provide explicit upper bounds for integral probability metrics and, at improved rates, a recently introduced Wasserstein metric for random graph distributions. The bounds are in terms of a vertex error term based on the Papangelou kernels of the vertex point processes and two edge error terms based on conditional edge probabilities. In addition to providing new tools for spatial random graphs along the way, such as a graph-based Georgii--Nguyen--Zessin formula, we also give applications of our bounds to the percolation graph of large balls in a Boolean model and to discretising a generalised random geometric graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02917 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stein's Method for Spatial Random Graphs Schuhmacher, Dominic Wirth, Leoni Carla Probability 05C80, 60E99, 60G55 In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main theorems provide explicit upper bounds for integral probability metrics and, at improved rates, a recently introduced Wasserstein metric for random graph distributions. The bounds are in terms of a vertex error term based on the Papangelou kernels of the vertex point processes and two edge error terms based on conditional edge probabilities. In addition to providing new tools for spatial random graphs along the way, such as a graph-based Georgii--Nguyen--Zessin formula, we also give applications of our bounds to the percolation graph of large balls in a Boolean model and to discretising a generalised random geometric graph. |
| title | Stein's Method for Spatial Random Graphs |
| topic | Probability 05C80, 60E99, 60G55 |
| url | https://arxiv.org/abs/2411.02917 |