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## Jérémie Bettinelli

École polytechnique
Laboratoire d'informatique (LIX)
91128 Palaiseau Cedex
FRANCE
E-mail: firstname « . » lastname « at » normalesup « . » org
Office: 2023
Phone: (+33) (0)1 77 57 80 61

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### Sketchfab folder – Picture folder

These simulations were done with Benoît Laslier. Instead of sampling plane quadrangulations unifromly at random, we use a different probability distribution and obtain quite different maps. The model is the following. We consider plane quadrangulations where each quadrangular face is given with one of the two possible diagonals. We can draw loops going around all the diagonals. We then choose a map with probability proportional to q to the power of the number of loops. Depending on the value of q, we observe different behaviors.

On the pictures, the loops are drawn in red and the edges of the quadrangulation are represented in black.

 FK 2.5k (q=0.5) [jpg1 – jpg2 – jpg3 – jpg4 – jpg5 – jpg6]

 FK weighted maps with 2 500 faces and parameter q=0.5
 FK 10k (q=2) [jpg1 – jpg2 – jpg3 – jpg4 – jpg5 – jpg6]

 FK weighted maps with 10 000 faces and parameter q=2 (Ising model)
 FK 5k (q=9) [jpg1 – jpg2 – jpg3 – jpg4 – jpg5 – jpg6]

 FK weighted maps with 5 000 faces and parameter q=9

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