A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is
We study random triangulations of the integer points [0, n] 2 ∩ Z 2 , where each triangulation σ has probability measure λ |σ | with λ > 0 being a real parameter and |σ | denoting the sum of the length of the edges in σ . Such triangulations are called lattice triangulations. We construct a height function on lattice triangulations and prove that, in the whole subcritical regime λ < 1, the function behaves as a Lyapunov function with respect to Glauber dynamics; that is, the function is adoi:10.1007/s00440-016-0735-z fatcat:2i2dfbuymjd3rcqpw7r6veac7m