Growing Random Sequences

Ilia Krasikov, Geoff Rodgers and Colin Tripp

We consider the random sequence x_n=x_{n-1}+\gamma x_q, with \gamma > 0, where q=0,1,...,n-1 is chosen randomly from a probability distribution P_n(q). When all q are chosen with equal probability, i.e. P_n(q)=1/n, we obtain an exact solution for the mean [x_n] and the divergence of the second moment [x_n^2] as functions of n and \gamma.

Journal of Physics A 37 2365 (2004).

Here are the files associated with this paper.

The ps file

Last updated 8 October 2003