On (a,b) pairs in random Fibonacci sequences
نویسندگان
چکیده
منابع مشابه
Random Fibonacci Sequences
We study the random Fibonacci tree, which is an infinite binary tree with non-negative numbers at each node defined as follows. The root consists of the number 1 with a single child also the number 1. Then we define the tree recursively in the following way: if x is the parent of y, then y has two children, namely |x−y| and x+y. This tree was studied by Benoit Rittaud [?] who proved that any pa...
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We study the random Fibonacci sequences defined by F1 = F2 = F̃1 = F̃2 = 1 and for n ≥ 1, Fn+2 = Fn+1 ± Fn (linear case) and F̃n+2 = |F̃n+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 the exponential growth of Fn for 0 < p ≤ 1, and of F̃n for 1/3 ≤ p ≤ 1 is almost surely given by ∫ ∞ 0 log ...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2018
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2018.03.002