Gallery of simulations

Sauron's eye

Pictures and movies of random lozenge tilings

[2016/08/20]

In Spring 2015 and Summer 2016 I used the Python and Mathematica as briefly described here to produce a number of pictures and “movies” of random lozenge tilings. Some of these pictures even appeared at an art exhibition at Harvard’s Radcliffe Institute accompanying Alexei Borodin’s fellowship.

These pictures and “movies” of random tilings are collected in this post.

Dear colleagues:

Feel free to use these pictures to illustrate your research in talks and papers, with attribution (CC BY-SA 4.0). Some of the images are available in very high resolution upon request.

Pictures and movies »

Fluctuations of the stochastic six vertex model

Simulations of stochastic higher spin vertex model

[2015/03/12]

The stochastic higher spin vertex model introduced in my paper with Ivan Corwin ([arXiv:1502.07374 [math.PR]][ivan6v]) generalizes the stochastic six vertex model considered by Borodin, Corwin, and Gorin, arXiv:1407.6729 [math.PR]. Here are some simulations related to this model.

Dear colleagues:

Feel free to use these pictures to illustrate your research in talks and papers, with attribution (CC BY-SA 4.0). Some of the images are available in very high resolution upon request.

View details »

Uniformly random tiling of a 9-gon

Implementation of Glauber dynamics simulation of random lozenge tilings

[2015/02/18]

I’ve implemented the Glauber dynamics to (approximately) sample uniformly random lozenge tilings of polygons of Gelfand-Tsetlin type. These polygons are called sawtooth domains by J. Novak. This paper by B. Laslier and F.L. Toninelli establishes rate of convergence of the Glauber dynamics to the uniformly random lozenge tiling.

See here the many results of the simulations.

Implementation »