The simplest example of a fragmentation process is the stick–breaking process,  More precisely, let us consider a stick of unit size and say that after an exponentially distributed time the stick breaks into two pieces of length β and 1 − β respectively. Then each of the resulting smaller sticks independently repeats the procedure and the process continues ad infinitum.

In mathematics and computer science, a random tree is a tree or arborescence that is formed by a stochastic process

In statistics, a Pólya urn model (also known as a Pólya urn scheme or simply as Pólya's urn)  is a type of statistical model used as an idealized mental exercise framework, unifying many treatments.