منابع مشابه
How do random Fibonacci sequences grow?
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 ...
متن کاملHow Do Random Fibonacci Sequences
We study the random Fibonacci sequences defined by F 1 = F 2 = e F 1 = e F 2 = 1 and for n ≥ 1, F n+2 = F n+1 ± Fn (linear case) and e F n+2 = | e F n+1 ± e Fn| (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 e Fn for 1/3 ≤ p ≤ 1 is almost surel...
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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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Using molecular simulations, we show that the aperiodic growth of quasicrystals is controlled by the ability of the growing quasicrystal nucleus to incorporate kinetically trapped atoms into the solid phase with minimal rearrangement. In the system under investigation, which forms a dodecagonal quasicrystal, we show that this process occurs through the assimilation of stable icosahedral cluster...
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Detailed growth paths of embryonic frog and chick axons were measured as the axons elongated in dispersed cultures on acid-rinsed glass surfaces. Mathematical analyses demonstrate that, under these conditions, axons do not grow randomly but tend to grow straight. Growth cones appear to actively alternate sides--right and left from the straight line of growth--and the growth cone neck exhibits a...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2007
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-007-0117-7