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arXiv · 1010.1086

Stochastic Flips on Two-letter Words

Olivier Bodini·Thomas Fernique·Damien Regnault
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Abstract

This paper introduces a simple Markov process inspired by the problem of quasicrystal growth. It acts over two-letter words by randomly performing \emph{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 fixed-point 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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BibTeXRIS

Olivier Bodini, Thomas Fernique, Damien Regnault. 2010-10-06. Stochastic Flips on Two-letter Words. https://arxiv.org/abs/1010.1086

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