Linear algebra of the permutation invariant Crow–Kimura model of prebiotic evolution

I uploaded to arXiv our joint text with Alexander Bratus and Yuri Semenov: arXiv:1306.0111. The text gives an interesting (in my humble opinion, of course) prospective on the problem of the error threshold. Using the fact that the mutation matrix ( in the paper’s notations) has a special structure, we were able to present several analytical results, without the usual resorting to limiting procedures when the genome length goes to infinity (cf. many statistical physics approaches to the problems of prebiotic evolution). Using these results we suggest to replace the vague speculative definitions of the error threshold with a rigorous one. The text has been submitted to the Bulletin of Mathematical Biology.

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