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 bijection1.

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 algorithm2. This random object exhibits an arctic circle phenomenon3.

The amoeba of a genus 1 Harnack curve blowing up.

  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