Almost-sure growth rate of generalized random Fibonacci sequences

Almost-sure Growth Rate of Generalized Random Fibonacci sequences

We study the generalized random Fibonacci sequences defined by their first nonnegative terms and for n ≥ 1, Fn+2 = λFn+1 ± Fn (linear case) and F̃n+2 = |λF̃n+1 ± F̃n| (non-linear case), where each ± sign is independent and either + with probability p or − with probability 1 − p (0 < p ≤ 1). Our main result is that, when λ is of the form λk = 2 cos(π/k) for some integer k ≥ 3, the exponential growt...

The Asymptotic Growth Rate of Random Fibonacci Type Sequences Ii

In this paper, we use ergodic theory to compute the aysmptotic growth rate of a family of random Fibonacci type sequences. This extends the result in [2]. We also prove some Lochs-type results regarding the effectiveness of various number theoretic expansions.

The Asymptotic Growth Rate of Random Fibonacci Type Sequences

Estimating the growth rate of random Fibonacci-type sequences is both challenging and fascinating. In this paper, by using ergodic theory, we prove a new result in this area. Let a denote an infinite sequence of natural numbers {a1, a2, · · · } and define a random Fibonaccitype sequence by f−1 = 0, f0 = 1, a0 = 0, and fk = 2fk−1 + 2fk−2 for k ≥ 1. Then, for almost all such infinite sequences a,...

Growth and Decay of Random Fibonacci Sequences

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On almost sure elimination of generalized quantifiers