Two Approaches to the Growth of Random Fibonacci Sequences

Abstract

This talk will extend some ideas from both Viswanath's and Rittaud’s work on random Fibonacci sequences. First, we will look at second order linear recurrence sequences whose coefficients belong to the set TeX Embedding failed! and form periodic cycles. We will analyze the growth of such sequences and develop criteria for determining whether a given sequence is bounded, grows linearly or grows exponentially. Second, we will derive the average growth rate of a random Fibonacci sequence through the use of binary trees and a Pascal-like array of numbers, for which we can further give an explicit formula.

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