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2016 Dynamics of lattice triangulations on thin rectangles
Pietro Caputo, Fabio Martinelli, Alistair Sinclair, Alexandre Stauffer
Electron. J. Probab. 21: 1-22 (2016). DOI: 10.1214/16-EJP4321

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 $\lambda =1$.

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Pietro Caputo. Fabio Martinelli. Alistair Sinclair. Alexandre Stauffer. "Dynamics of lattice triangulations on thin rectangles." Electron. J. Probab. 21 1 - 22, 2016. https://doi.org/10.1214/16-EJP4321

Information

Received: 22 May 2015; Accepted: 4 April 2016; Published: 2016
First available in Project Euclid: 14 April 2016

zbMATH: 1336.60183
MathSciNet: MR3492933
Digital Object Identifier: 10.1214/16-EJP4321

Subjects:
Primary: 60K35

JOURNAL ARTICLE
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