| Full text | |
| Author(s): |
Coletti, Cristian F.
;
De Lima, Lucas R.
;
Hinsen, Alexander
;
Jahnel, Benedikt
;
Valesin, Daniel
Total Authors: 5
|
| Document type: | Journal article |
| Source: | JOURNAL OF APPLIED PROBABILITY; v. N/A, p. 19-pg., 2023-04-24. |
| Abstract | |
Let a random geometric graph be defined in the supercritical regime for the existence of a unique infinite connected component in Euclidean space. Consider the first-passage percolation model with independent and identically distributed random variables on the random infinite connected component. We provide sufficient conditions for the existence of the asymptotic shape, and we show that the shape is a Euclidean ball. We give some examples exhibiting the result for Bernoulli percolation and the Richardson model. In the latter case we further show that it converges weakly to a nonstandard branching process in the joint limit of large intensities and slow passage times. (AU) | |
| FAPESP's process: | 20/12868-9 - Limiting shape for the contact process on random geometric graphs |
| Grantee: | Lucas Roberto de Lima |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |
| FAPESP's process: | 17/10555-0 - Stochastic modeling of interacting systems |
| Grantee: | Fabio Prates Machado |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 19/19056-2 - Asymptotic shape for subadditive processes on groups and on random geometric graphs |
| Grantee: | Lucas Roberto de Lima |
| Support Opportunities: | Scholarships in Brazil - Doctorate |