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Lower deviation probabilities for supercritical Galton–Watson processes☆
There is a well-known sequence of constants cn describing the growth of supercritical Galton–Watson processes Zn. By lower deviation probabilities we refer to P(Zn=kn) with kn=o(cn) as n increases. We give a detailed picture of the asymptotic behavior of such lower deviation probabilities. This complements and corrects results known from …