Growth and Structure of Stochastic Sequences
arXiv:cond-mat/0208072 · doi:10.1088/0305-4470/35/41/101
Abstract
We introduce a class of stochastic integer sequences. In these sequences, every element is a sum of two previous elements, at least one of which is chosen randomly. The interplay between randomness and memory underlying these sequences leads to a wide variety of behaviors ranging from stretched exponential to log-normal to algebraic growth. Interestingly, the set of all possible sequence values has an intricate structure.
4 pages, 4 figures