Growth and Structure of Stochastic Sequences

Details Growth and Structure of Stochastic Sequences Growth and Structure of Stochastic Sequences

2002-08-05

arxiv.org/abs/cond-mat/0208072v1

J. Phys. A 35, L557 (2002)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures

Scientific paper

10.1088/0305-4470/35/41/101

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.

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