## Mathematical gallery

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

### Tiling with dominos and rhombi

A uniform tiling of an Aztec diamond of size 160 with dominos. Here is a link to a vector graphics rendering of the same image.

A tiling of an Aztec rectangle with special boundary conditions with periodic weights along each row. This is an example of a Schur process. Here is a link to a vector graphics rendering of the same image.

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

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

### Other models from combinatorics and statistical mechanics

A piece of an infinite isoradial graph (in black) and the underlying quadgraph, providing a tiling of the plane with rhombi.

### Spectral curves

The amoeba of a genus 1 Harnack curve blowing up, related to the temperature change in the Ising model.

## 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