In some cases the analysis of random binary trees under the random permutation model can be automatically transferred to the uniform model.

In computer science and probability theory, a random binary tree refers to a binary tree selected at random from some probability distribution on binary trees.

Types of random trees include uniform spanning tree, random minimal spanning tree, random binary tree, treap, rapidly exploring random tree, Brownian tree, and random forest.

In applications of binary search tree data structures, it is rare for the values in the tree to be inserted without deletion in a random order, limiting the direct applications of random binary trees.