Precise logarithmic asymptotics for the right tails of some limit random variables for random trees
| dc.creator | Fill, James Allen | |
| dc.creator | Janson, Svante | |
| dc.date | 2007-01-09 | |
| dc.date.accessioned | 2026-07-07T07:39:27Z | |
| dc.date.available | 2026-07-07T07:39:27Z | |
| dc.description | For certain random variables that arise as limits of functionals of random finite trees, we obtain precise asymptotics for the logarithm of the right-hand tail. Our results are based on the facts (i) that the random variables we study can be represented as functionals of a Brownian excursion and (ii) that a large deviation principle with good rate function is known explicitly for Brownian excursion. Examples include limit distributions of the total path length and of the Wiener index in conditioned Galton-Watson trees (also known as simply generated trees). In the case of Wiener index (where we recover results proved by Svante Janson and Philippe Chassaing by a different method) and for some other examples, a key constant is expressed as the solution to a certain optimization problem, but the constant's precise value remains unknown. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701259 | |
| dc.identifier | http://arxiv.org/abs/math/0701259 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121456 | |
| dc.subject | Probability | |
| dc.subject | 60F10; 60C05, 60J65 | |
| dc.title | Precise logarithmic asymptotics for the right tails of some limit random variables for random trees | |
| dc.type | text |