The density of the ISE and local limit laws for embedded trees

dc.creatorBousquet-Mélou, Mireille
dc.creatorJanson, Svante
dc.date2005-09-14
dc.date2006-04-10
dc.date.accessioned2026-07-07T09:36:46Z
dc.date.available2026-07-07T09:36:46Z
dc.descriptionIt 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.identifierhttps://arxiv.org/abs/math/0509322
dc.identifierhttp://arxiv.org/abs/math/0509322
dc.identifierThe Annals of Applied Probability 16, 3 (2006) 1597--1632
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160234
dc.subjectProbability
dc.subjectCombinatorics
dc.subject60C05 (Primary), 05A15, 05C05 (Secondary)
dc.titleThe density of the ISE and local limit laws for embedded trees
dc.typetext

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