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• W3136189605 abstract "In this paper we prove an extreme value law for a stochastic process obtained by iterating the Rényi map x ↦ β x ( mod 1 ) , where we assume that β > 1 is an integer. Haiman (2018) derived a recursion formula for the Lebesgue measure of threshold exceedance sets. We show how this recursion formula is related to a rescaled version of the k -generalized Fibonacci sequence. For the latter sequence we derive a Binet formula which leads to a closed-form expression for the distribution of partial maxima of the stochastic process. The proof of the extreme value law is completed by deriving sharp bounds for the dominant root of the characteristic polynomial associated with the Fibonacci sequence." @default.
• W3136189605 created "2021-03-29" @default.
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• W3136189605 date "2021-05-01" @default.
• W3136189605 modified "2023-09-27" @default.
• W3136189605 title "Generalized Fibonacci numbers and extreme value laws for the Rényi map" @default.
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• W3136189605 doi "https://doi.org/10.1016/j.indag.2021.03.002" @default.
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