Growth and Structure of Stochastic Sequences
Statistical Mechanics
2007-05-23 v1 Disordered Systems and Neural Networks
Probability
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.
Keywords
Cite
@article{arxiv.cond-mat/0208072,
title = {Growth and Structure of Stochastic Sequences},
author = {E. Ben-Naim and P. L. Krapivsky},
journal= {arXiv preprint arXiv:cond-mat/0208072},
year = {2007}
}
Comments
4 pages, 4 figures