Growth rate for the expected value of a generalized random Fibonacci sequence
| dc.creator | Janvresse, Elise | |
| dc.creator | Rittaud, Benoît | |
| dc.creator | De La Rue, Thierry | |
| dc.date | 2008-04-15 | |
| dc.date.accessioned | 2026-07-07T12:37:08Z | |
| dc.date.available | 2026-07-07T12:37:08Z | |
| dc.description | 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 = |λg_{n-1} +/- g_{n-2} |. When λ>=2 and 0 < p <= 1, we prove that the expected value of g_n grows exponentially fast. When λ= λ_k = 2 cos(π/k) for some fixed integer k>2, we show that the expected value of g_n grows exponentially fast for p>(2-λ_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. | |
| dc.identifier | https://arxiv.org/abs/0804.2400 | |
| dc.identifier | http://arxiv.org/abs/0804.2400 | |
| dc.identifier | Journal of Physics A Mathematical and Theoretical 42 (2009) 085005 | |
| dc.identifier | doi:10.1088/1751-8113/42/8/085005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218334 | |
| dc.subject | Probability | |
| dc.subject | 11A55, 15A52 (Primary); 05c05, 15A35 (Secondary) | |
| dc.title | Growth rate for the expected value of a generalized random Fibonacci sequence | |
| dc.type | text |