Schur process style parameters $x_1,\ldots,x_n$ and $y_1,\ldots,y_n$ determine the probability distribution on domino tilings of the Aztec diamond; the sampling is done via shuffling algorithm by Betea-Boutillier-Bouttier-Chapuy-Corteel-Vuletic.

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▶ Partitions forming the Schur process (click to expand)

No subset data available yet. Click "Sample" to generate.

See also:

• https://math.mit.edu/~borodin/aztec_phenomena.html
• arXiv:1407.3764 — D. Betea, C. Boutillier, J. Bouttier, G. Chapuy, S. Corteel, and M. Vuletic, Perfect sampling algorithms for Schur processes, Markov Process. Related Fields 24 (2018), no. 3, 381–418.

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code

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

• Link to code (This simulation is interactive, written in JavaScript)
• Link to code (C++ code for the simulation)

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