Expansion-modification system: stationary measures and asymptotic scaling

Details Expansion-modification system: stationary measures and asymptotic scaling Expansion-modification system: stationary measures and asymptotic scaling

2012-02-12

arxiv.org/abs/1202.2549v1

Mathematics

Probability

21 pages, 2 figures

Scientific paper

This work is devoted to the study of the stationary measures of the expansion--modification model. We prove all initial distributions converge towards a unique stationary measure exhibiting decay of correlations. We also develop an argument towards the proof of an asymptotic scaling behavior for the correlation function, which allows us to give a closed expression for the scaling exponent as a function of the mutation probability. Finally, we prove the validity of the asymptotic scaling behavior and the corresponding expression for scaling exponents, for low mutation probability.

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