Fluctuations of q-Weighted Domino Tilings     domino-tilings

Leonid Petrov


Simulation Info

Fluctuations of q-Weighted Domino Tilings     domino-tilings

Leonid Petrov

Interactive simulation studying fluctuations of boundary paths in q-Whittaker weighted domino tilings of the Aztec diamond. Sample many tilings via RSK, extract nonintersecting lattice paths, and visualize fluctuation histograms of the outermost path height.

k=10
Samples: 0  |  Mean: —  |  SD: —  |  Skew: —  |  Kurt: —  |  JB: —
Stats legend SD = standard deviation. Skew = skewness (0 for symmetric). Kurt = excess kurtosis (0 for normal). JB = Jarque-Bera normality test: JB = n/6·(S² + K²/4), p from χ²(2). [TW] = Tracy-Widom F₂ reference: skew 0.224, excess kurt 0.093. Histogram overlays: red solid = TW F₂, green dashed = Gaussian (Edgeworth expansion, matched to empirical SD).
Scaling test

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 (opens in new tab)). 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