Branching random walk

In probability theory, a branching random walk is a stochastic process whose value at any point in discrete time is a set of point in some space, such as the real line, such that each point may have one or more descendants at the next point in time, located at places resulting from addition of a random variable to the location of their parents.

For example, for a binary branching random walk, suppose X₀ = 0, and X_1,1 and X_1,2 are the two children of X₀, and are indenpendent N(0, 1) random variables. Then at time 2, X_2,1 and X_2,2 would be the sum of X_1,1 and a N(0, 1) random variable, and X_2,1 and X_2,1 would be the sum of X_1,2 and a N(0, 1) random variable, and so on.