Menu:

Here are results of my attempts to simulate random combinatorical objects related to my research interests.

boxed plane partition

A uniform boxed plane partition with a large number of boxes, generated using Boltzmann samplers and Pak’s bijection[1].

plane partition

A uniform plane partition, obtained with the same technique. Some problems in the implementation for small values…​

hexagon

A uniform tiling of a 30x30x30 hexagon by lozenges, generated using Propp and Wilson coupling from the past algorithm.

grove

A uniform grove of size 100 generated by the grove shuffling algorithm[2]. This random object exhibits an arctic circle phenomenon[3].

The evolution of a family of amoebas of genus 1 curves

The amoeba of a genus 1 Harnack curve blowing up.

References

[1] Random Sampling of Plane Partitions, O. Bodini, É. Fusy and C. Pivoteau, Combinatorics, Probability and Computing (2010), 19: 201—​226)

[2] The Cube Reccurrence, Gabriel D. Carroll, David E Speyer

[3] An arctic circle theorem for groves, T. K. Petersen, D. Speyer