Editing Brownian tree (section)

{{Short description|Concept in probability theory}}
{{About|the Continuum Random Tree obtained from a Brownian excursion|the computer art developed in the 90s|Diffusion-limited aggregation}}
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{{refimprove|date=December 2022}}
{{original research|date=December 2022}}
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In [[probability theory]], the '''Brownian tree''', or '''Aldous tree''', or '''Continuum Random Tree (CRT)'''<ref>{{Cite book |last=Le Gall |first=Jean-François |title=Spatial branching processes, random snakes, and partial differential equations |publisher=Springer Science \& Business Media |year=1999}}</ref> is a random [[real tree]] that can be defined from a [[Brownian excursion]]. The Brownian tree was defined and studied by [[David Aldous]] in three articles published in 1991 and 1993. This tree has since then been generalized.

This random tree has several equivalent definitions and constructions:<ref>{{cite web|title=The continuum random tree|url=http://www.stat.berkeley.edu/~aldous/Research/research-crt.html|author=David Aldous|access-date=2012-02-10|publication-date=}}</ref> using sub-trees generated by finitely many leaves, using a Brownian excursion, Poisson separating a straight line or as a limit of Galton-Watson trees.

Intuitively, the Brownian tree is a binary tree whose nodes (or branching points) are [[Dense set|dense]] in the tree; which is to say that for any distinct two points of the tree, there will always exist a node between them. It is a [[fractal]] object which can be approximated with computers<ref>{{cite web|title=Une simulation de l'arbre continu aléatoire brownien|url=http://www.math.u-psud.fr/~miermont/simul.php|author=[[Grégory Miermont]]|access-date=2012-02-10|publication-date=|archive-date=2016-03-03|archive-url=https://web.archive.org/web/20160303172928/http://www.math.u-psud.fr/~miermont/simul.php|url-status=dead}}</ref> or by physical processes with [[Dendrite (crystal)|dendritic structures]].