# Growth rate for the expected value of a generalized random Fibonacci sequence

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1 LMRS - Laboratoire de Mathématiques Raphaël Salem 2 LMPT - Laboratoire de Mathématiques et Physique Théorique 3 LAGA - Laboratoire Analyse, Géométrie et Applications

Abstract : A random Fibonacci sequence is defined by the relation g n = | g {n-1} +- g {n-2} |, where the +- sign is chosen by tossing a balanced coin for each n. We generalize these sequences to the case when the coin is unbalanced denoting by p the probability of a +, and the recurrence relation is of the form g n = |\lambda g {n-1} +- g {n-2} |. When \lambda >=2 and 0 < p 2, we show that the expected value of g n grows exponentially fast for p>2-\lambda k-4 and give an algebraic expression for the growth rate. The involved methods extend and correct those introduced in a previous paper by the second author.

Keywords : binary tree random Fibonacci sequence random Fibonacci tree linear recurring sequence Hecke group

Autor: Elise Janvresse - Benoît Rittaud - Thierry De La Rue -

Fuente: https://hal.archives-ouvertes.fr/

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