Random Fibonacci sequences and the number $1.13198824\dots$
Open Access
- 10 June 1999
- journal article
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 69 (231) , 1131-1156
- https://doi.org/10.1090/s0025-5718-99-01145-x
Abstract
For the familiar Fibonacci sequence (defined by , and for 2$" src="/mcom/2000-69-231/S0025-5718-99-01145-X/gif-abstract/img36.gif" height="28" width="47">), increases exponentially with at a rate given by the golden ratio . But for a simple modification with both additions and subtractions - the random Fibonacci sequences defined by , and for 2$" src="/mcom/2000-69-231/S0025-5718-99-01145-X/gif-abstract/img41.gif" height="28" width="47">, , where each sign is independent and either or - with probability - it is not even obvious if should increase with . Our main result is thatKeywords
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