Uniform temporal trees
Motivated by the study of random temporal networks, we introduce a class of random trees that we coin uniform temporal trees. A uniform temporal tree is obtained by assigning independent uniform [0, 1] labels to the edges of a rooted complete infinite -ary tree and keeping only those vertices for wh...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Pompeu Fabra |
| Repositorio: | Repositorio Digital de la UPF |
| OAI Identifier: | oai:repositori.upf.edu:10230/72167 |
| Acceso en línea: | https://hdl.handle.net/10230/72167 http://dx.doi.org/10.1002/rsa.70040 |
| Access Level: | acceso abierto |
| Palabra clave: | Random temporal trees Random trees Temporal graphs |
| Sumario: | Motivated by the study of random temporal networks, we introduce a class of random trees that we coin uniform temporal trees. A uniform temporal tree is obtained by assigning independent uniform [0, 1] labels to the edges of a rooted complete infinite -ary tree and keeping only those vertices for which the path from the root to the vertex has decreasing edge labels. The -percolated uniform temporal tree, denoted by T ,, is obtained similarly, with the additional constraint that the edge labels on each path are all below . We study several properties of these trees, including their size, height, the typical depth of a vertex, and degree distribution. In particular, we establish a limit law for the size of T , which states that ∣T ,∣ np converges in distribution to an Exponential(1) random variable as → ∞. For the height ,, we prove that , np converges to in probability. Uniform temporal trees show some remarkable similarities to uniform random recursive trees. |
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