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

Growth rate for the expected value of a generalized random Fibonacci sequence - Download this document for free, or read online. Document in PDF available to download.

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

Author: ** Elise Janvresse - Benoît Rittaud - Thierry De La Rue - **

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