Stochastic Flips on Dimer Tilings - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2010

Stochastic Flips on Dimer Tilings

Abstract

This paper introduces a Markov process inspired by the problem of quasicrystal growth. It acts over dimer tilings of the triangular grid by randomly performing local transformations, called $\textit{flips}$, which do not increase the number of identical adjacent tiles (this number can be thought as the tiling energy). Fixed-points of such a process play the role of quasicrystals. We are here interested in the worst-case expected number of flips to converge towards a fixed-point. Numerical experiments suggest a $\Theta (n^2)$ bound, where $n$ is the number of tiles of the tiling. We prove a $O(n^{2.5})$ upper bound and discuss the gap between this bound and the previous one. We also briefly discuss the average-case.
Fichier principal
Vignette du fichier
dmAM0115.pdf (1.16 Mo) Télécharger le fichier
Origin : Publisher files allowed on an open archive
Loading...

Dates and versions

hal-01185602 , version 1 (20-08-2015)

Identifiers

Cite

Thomas Fernique, Damien Regnault. Stochastic Flips on Dimer Tilings. pp.205-218, ⟨10.46298/dmtcs.2803⟩. ⟨hal-01185602⟩
81 View
446 Download

Altmetric

Share

Gmail Facebook X LinkedIn More