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)-
Link to code(JavaScript simulation with RSK WASM sampling engine)