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A Lyapunov function for Glauber dynamics on lattice triangulations

2016
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Probability theory and related fields
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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 a

doi:10.1007/s00440-016-0735-z
fatcat:2i2dfbuymjd3rcqpw7r6veac7m