A restricted random walk defined via a Fibonacci process

Martin Griffiths

    Research output: Contribution to journalArticlepeer-review

    Abstract

    In this article we study a random walk on a particularly simple graph. This walk is determined by a probabilistic process associated with the Fibonacci sequence. Exact formulas are derived for the expected proportions of time spent on each arc of the graph for a walk of length n, giving rise to sequences that do not appear in Sloane's On-Line Encyclopedia of Integer Sequences. We also obtain asymptotic relations for these expected proportions.
    Original languageEnglish
    Pages (from-to)1-11
    Number of pages10
    JournalJournal of Integer Sequences
    Volume14
    Issue number5
    Publication statusPublished - 2011

    Keywords

    • Fibonacci numbers
    • Generating functions
    • Probabilities
    • Random walks

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