Simulations

Massive Loop Erased Random Walk

Three samples from a loop-erased random walk on a hexagon-shaped piece of a directed triangular lattice with side-length 500. On the right the drift is zero, and therefore this is an approximation of SLE_2, the two walks on the right have a small and a large drift to the right respectively and are therefore approximations of drifted SLE_2.

Temperley bijection for the hexagonal lattice

One sample from a dimer measure together with it's primal and dual Temperley trees on the left and the corresponding lozenge tiling on the right.

Uniform Spanning Tree

A uniform spanning tree generated with Wilson's algorithm, with several marked branches. Each of the branches is approximately an SLE_2 to the boundary.

Stochastic six vertex model

Simulations of the stochastic six vertex model, made together with Hindy Drillick, based on code from Leonid Petrov, which can be found at: https://github.com/lenis2000/simulations

From left to right:

1. A simulation of the multispecies stochastic six vertex model on a 400x400 square, where on each position there is an incoming particle with a unique class, in ascending order. Each pixel is colored with a color corresponding to the class of the outcoming arrow to the right at that vertex. The parameters are b1=0.2 and b2=0.7

2. With the same parameters and classes on a 800x800 square, the trace of the 25 particles starting closest to the origin.

3. 4000 Simulations of the angles of the trajectories of the two particles closest to the origin on a 300x300 square with b1=0.1 and b2=0.8