%0 Journal Article
%T Growth rate for the expected value of a generalized random Fibonacci sequence
%A Elise Janvresse
%A Beno£¿t Rittaud
%A Thierry De La Rue
%J Mathematics
%D 2008
%I arXiv
%R 10.1088/1751-8113/42/8/085005
%X 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 <= 1, we prove that the expected value of g_n grows exponentially fast. When \lambda = \lambda_k = 2 cos(\pi/k) for some fixed integer k>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.
%U http://arxiv.org/abs/0804.2400v1