Stochastic Flips on Two-letter Words

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(n3 ) in the worst-case and by O(n5/2 ln n) in the average-case, where n denotes the length of the initial word.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Olivier Bodini, Thomas Fernique, Damien Regnault
• Keywords: Consecutive Identical Letters, CORR 2010, Education, FLIPS, Simple Markov Process