The density of the ISE and local limit laws for embedded trees
| dc.creator | Bousquet-Mélou, Mireille | |
| dc.creator | Janson, Svante | |
| dc.date | 2005-09-14 | |
| dc.date | 2006-04-10 | |
| dc.date.accessioned | 2026-07-07T09:36:46Z | |
| dc.date.available | 2026-07-07T09:36:46Z | |
| dc.description | It has been known for a few years that the occupation measure of several models of embedded trees converges, after a suitable normalization, to the random measure called ISE (Integrated SuperBrownian Excursion). Here, we prove a local version of this result: ISE has a (random) Hölder continuous density, and the vertical profile of embedded trees converges to this density, at least for some such trees. As a consequence, we derive a formula for the distribution of the density of ISE at a given point. This follows from earlier results by Bousquet-Mélou on convergence of the vertical profile at a fixed point. We also provide a recurrence relation defining the moments of the (random) moments of ISE. | |
| dc.identifier | https://arxiv.org/abs/math/0509322 | |
| dc.identifier | http://arxiv.org/abs/math/0509322 | |
| dc.identifier | The Annals of Applied Probability 16, 3 (2006) 1597--1632 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160234 | |
| dc.subject | Probability | |
| dc.subject | Combinatorics | |
| dc.subject | 60C05 (Primary), 05A15, 05C05 (Secondary) | |
| dc.title | The density of the ISE and local limit laws for embedded trees | |
| dc.type | text |