The density of the ISE and local limit laws for embedded trees
Bousquet-Mélou, Mireille ; Janson, Svante
Ann. Appl. Probab., Tome 16 (2006) no. 1, p. 1597-1632 / Harvested from Project Euclid
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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.
Publié le : 2006-08-14
Classification:  Random binary tree,  natural labeling,  vertical profile,  ISE,  local limit law,  60C15,  05A15,  05C05 
@article{1159804993,
     author = {Bousquet-M\'elou, Mireille and Janson, Svante},
     title = {The density of the ISE and local limit laws for embedded trees},
     journal = {Ann. Appl. Probab.},
     volume = {16},
     number = {1},
     year = {2006},
     pages = { 1597-1632},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1159804993}
}

Bousquet-Mélou, Mireille; Janson, Svante. The density of the ISE and local limit laws for embedded trees. Ann. Appl. Probab., Tome 16 (2006) no. 1, pp.  1597-1632. http://gdmltest.u-ga.fr/item/1159804993/