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Article overview
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Dynamics of Lattice Triangulations on Thin Rectangles | Pietro Caputo
; Fabio Martinelli
; Alistair Sinclair
; Alexandre Stauffer
; | Date: |
22 May 2015 | Abstract: | We consider random lattice triangulations of $n imes k$ rectangular regions
with weight $lambda^{|sigma|}$ where $lambda>0$ is a parameter and
$|sigma|$ denotes the total edge length of the triangulation. When
$lambdain(0,1)$ 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 $lambda=1$. | Source: | arXiv, 1505.6161 | Services: | Forum | Review | PDF | Favorites |
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