Dynamics of lattice triangulations on thin rectangles

Pietro Caputo, Fabio Martinelli, Alistair Sinclair, Alexandre Stauffer

Research output: Contribution to journalArticle

4 Citations (Scopus)
124 Downloads (Pure)

Abstract

We consider random lattice triangulations of $n\times k$ rectangular regions with weight $\lambda^{|\sigma|}$ where $\lambda>0$ is a parameter and $|\sigma|$ denotes the total edge length of the triangulation. When $\lambda\in(0,1)$ and $k$ is fixed, we prove a tight upper bound of order $n^2$ for the mixing time of the edge-flip Glauber dynamics. Combined with the previously known lower bound of order $\exp(\Omega(n^2))$ for $\lambda>1$ [3], this establishes the existence of a dynamical phase transition for thin rectangles with critical point at $\lambda=1$.
Original languageEnglish
Pages (from-to)1-22
JournalElectronic Journal of Probability
Volume21
DOIs
Publication statusPublished - 14 Apr 2016

Keywords

  • math.PR
  • cs.DM
  • math.CO

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