## Mathematical gallery

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

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

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

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

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

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