A dynamical-system picture of a simple branching-process phase transition

Details A dynamical-system picture of a simple branching-process phase transition A dynamical-system picture of a simple branching-process phase transition

2010-11-30

arxiv.org/abs/1011.6513v1

Mathematics

Probability

18 pages. In: Bingham, N. H., and Goldie, C. M. (eds), Probability and Mathematical Genetics: Papers in Honour of Sir John Kin

Scientific paper

This paper develops ideas from a previous paper described as `an appetizer for non-linear Wiener--Hopf theory', but is completely independent of that paper. It again considers only the simplest possible case in which the underlying motion of the branching particles is described by a two-state Markov chain. Key generating functions provide solutions of a simple two-dimensional dynamical system, and the main interest is in the way in which Probability Theory and ODE theory complement each other. ODE pictures convey rather strikingly a simple phase transition. No knowledge of either ODE theory or Wiener--Hopf theory is assumed.

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