Stochastic Flips on Two-letter Words

Abstract : This paper introduces a simple Markov process inspired by the problem of quasicrystal growth. It acts over two-letter words by randomly performing flips, a local transformation which exchanges two consecutive different letters. More precisely, only the flips which do not increase the number of pairs of consecutive identical letters are allowed. Fixed-points of such a process thus perfectly alternate different letters. We show that the expected number of flips to converge towards a fixedpoint is bounded by O(n^3) in the worst-case and by O(n^(5/2) ln n) in the average-case, where n denotes the length of the initial word.
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Olivier Bodini, Thomas Fernique, Damien Regnault. Stochastic Flips on Two-letter Words. ANALCO 2010 - 7th Workshop on Analytic Algorithmics and Combinatorics, Jan 2010, Austin, TX, United States. pp.48-55, ⟨10.1137/1.9781611973006.7⟩. ⟨hal-00436516⟩

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