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Growth and structure of stochastic sequences

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Published 1 October 2002 • Published under licence by IOP Publishing Ltd
, , Citation E Ben-Naim and P L Krapivsky 2002 J. Phys. A: Math. Gen. 35 L557 DOI 10.1088/0305-4470/35/41/101

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Author affiliations

1 Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

2 Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA

Dates

  1. Received 9 August 2002
  2. Published

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0305-4470/35/41/L557

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 behaviours 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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