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In probability theory, the Brownian tree, or Aldous tree, or Continuum Random Tree (CRT)[1] 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:[2] 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 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[3] or by physical processes with dendritic structures.
- ^ Le Gall, Jean-François (1999). Spatial branching processes, random snakes, and partial differential equations. Springer Science \& Business Media.
- ^ David Aldous. "The continuum random tree". Retrieved 2012-02-10.
- ^ Grégory Miermont. "Une simulation de l'arbre continu aléatoire brownien". Archived from the original on 2016-03-03. Retrieved 2012-02-10.