Flip dynamics in octagonal rhombus tiling sets
Résumé
We investigate the properties of classical single flip dynamics in sets of two-dimensional random rhombus tilings. Single flips are local moves involving 3 tiles which sample the tiling sets via Monte Carlo Markov chains. We determine the ergodic times of these dynamical systems (at infinite temperature): they grow with the system size N_T like Cst. N_T^2 ln N_T; these dynamics are rapidly mixing. We use an inherent symmetry of tiling sets and a powerful tool from probability theory, the coupling technique. We also point out the interesting occurrence of Gumbel distributions.