Erdős–Rényi Poissonized
We introduce a variant of the Erdős–Rényi random graph where the number of vertices is random and follows a Poisson law. A very simple Markov property of the model entails that the Lukasiewicz exploration is made of independent Poisson increments. Using a vanilla Poisson counting process, this enabl...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-07-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.578/ |
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| _version_ | 1825206230959783936 |
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| author | Curien, Nicolas |
| author_facet | Curien, Nicolas |
| author_sort | Curien, Nicolas |
| collection | DOAJ |
| description | We introduce a variant of the Erdős–Rényi random graph where the number of vertices is random and follows a Poisson law. A very simple Markov property of the model entails that the Lukasiewicz exploration is made of independent Poisson increments. Using a vanilla Poisson counting process, this enables us to give very short proofs of classical results such as the phase transition for the giant component or the connectedness for the standard Erdős–Rényi model. |
| format | Article |
| id | doaj-art-58481a7b79ab485a851deb2ea2a0b671 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-58481a7b79ab485a851deb2ea2a0b6712025-02-07T11:21:51ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-07-01362G664965610.5802/crmath.57810.5802/crmath.578Erdős–Rényi PoissonizedCurien, Nicolas0Université Paris-SaclayWe introduce a variant of the Erdős–Rényi random graph where the number of vertices is random and follows a Poisson law. A very simple Markov property of the model entails that the Lukasiewicz exploration is made of independent Poisson increments. Using a vanilla Poisson counting process, this enables us to give very short proofs of classical results such as the phase transition for the giant component or the connectedness for the standard Erdős–Rényi model.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.578/ |
| spellingShingle | Curien, Nicolas Erdős–Rényi Poissonized Comptes Rendus. Mathématique |
| title | Erdős–Rényi Poissonized |
| title_full | Erdős–Rényi Poissonized |
| title_fullStr | Erdős–Rényi Poissonized |
| title_full_unstemmed | Erdős–Rényi Poissonized |
| title_short | Erdős–Rényi Poissonized |
| title_sort | erdos renyi poissonized |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.578/ |
| work_keys_str_mv | AT curiennicolas erdosrenyipoissonized |