## Sharp asymptotic results for simplified mutation-selection algorithms.(English)Zbl 1036.60026

The authors study the asymptotic behaviour of a mutation-selection genetic algorithm on the integers with finite population of size $$p$$. The mutation is defined by the steps of a simple random walk and the fitness function is linear. The authors prove that the normalized population satisfies an invariance principle, that a large deviations principle holds and that the relative positions converge in law as well as that after $$n$$ steps, the population is asymptotically around $$\sqrt{n}$$ times the position at time 1 of a Bessel process of dimension $$2p-1$$.

### MSC:

 60F17 Functional limit theorems; invariance principles 60F10 Large deviations 92D15 Problems related to evolution 60F05 Central limit and other weak theorems

MersenneTwister
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### References:

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