Random tree growth with general weight function
| dc.creator | Rudas, Anna | |
| dc.date | 2004-10-25 | |
| dc.date.accessioned | 2026-07-07T05:13:41Z | |
| dc.date.available | 2026-07-07T05:13:41Z | |
| dc.description | We extend the results of B. Bollobas, O. Riordan, J. Spencer, G. Tusnady, and Mori. We consider a model of random tree growth, where at each time unit a new node is added and attached to an already existing node chosen at random. The probability with which a node with degree $k$ is chosen is proportional to $w(k)$, where $w$ is a fixed weight function. We prove that if $w$ fulfills some asymptotic requirements then the degree sequence converges in probability, we give the limit. In particular if $w$ is asymptotically linear then the degree sequence decays with power law. Our method of proof is analytic rather than combinatorial, having the advantage of robustness: only asymptotic properties of the weight function $w$ are used, while in the cited papers the explicit law $w(k)=ak+b$ is assumed. | |
| dc.description | 17 pages, no figures, submitted to Random Structures and Algorithms | |
| dc.identifier | https://arxiv.org/abs/math/0410532 | |
| dc.identifier | http://arxiv.org/abs/math/0410532 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72999 | |
| dc.subject | Probability | |
| dc.title | Random tree growth with general weight function | |
| dc.type | text |