Displays a colored domino tiling of an Aztec diamond sampled with Schur process weights. Parameters x and y control the probability measure connected to representation theory. Controls set the diamond size, uniform or r-weighted presets, and individual x/y parameter lists.
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.
▶ 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.
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)