Stochastic Colored Six-Vertex Model     vertex-models

Leo Petrov


Simulation Info

Stochastic Colored Six-Vertex Model     vertex-models

Leo Petrov

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Description

The stochastic colored six-vertex model is an 𝔰𝔩n+1-related integrable stochastic system on a square lattice. Each path carries a "color" (an integer label), and at each vertex, two incoming paths (from the left and bottom) interact and produce two outgoing paths (going up and right) according to probabilistic rules.

The stochastic weights depend on the relative ordering of the incoming colors:

The boundary conditions place paths with colors 0, 1, 2, ..., N−1 entering from the left boundary at heights 0, 1, 2, ..., N−1, respectively. The rainbow coloring visualizes how these colored paths interact, cross, and separate as they evolve through the lattice, revealing the characteristic "arctic curve" phenomenon where paths freeze into deterministic regions.

References


code

(note: parameters in the code might differ from the ones in simulation results below)

Dear colleagues:
Feel free to use code (unless otherwise specified next to the corresponding link), data, and visualizations to illustrate your research in talks and papers, with attribution (CC BY-SA 4.0). Some images are available in very high resolution upon request. I can also produce other simulations upon request - email me at lenia.petrov@gmail.com
This material is based upon work supported by the National Science Foundation under Grant DMS-2153869