Recursive self-similarity for a random object is the property of being decomposable into independent rescaled copies of the original object. Certain random combinatorial objects--trees and triangulations--possess approximate versions of recursive self-similarity, and then their continuous limits possess exact recursive self-similarity. In particular, since the limit continuum random tree can be identified with Brownian excursion, we get a nonobvious recursive self-similarity property for Brownian excursion.
Publié le : 1994-04-14
Classification:
Self-similarity,
recursive,
random tree,
random triangulation,
Brownian excursion,
weak convergence,
centroid,
continuum tree,
60C05,
60B10,
60J65
@article{1176988720,
author = {Aldous, David},
title = {Recursive Self-Similarity for Random Trees, Random Triangulations and Brownian Excursion},
journal = {Ann. Probab.},
volume = {22},
number = {4},
year = {1994},
pages = { 527-545},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988720}
}
Aldous, David. Recursive Self-Similarity for Random Trees, Random Triangulations and Brownian Excursion. Ann. Probab., Tome 22 (1994) no. 4, pp. 527-545. http://gdmltest.u-ga.fr/item/1176988720/