This simulation generates random tilings with random edge weights via the shuffling algorithm. The original python code was created by Sunil Chhita; this version is adapted for JS + WebAssembly. The sampler works in your browser. Up to $n \sim 120$ it works in reasonable time, but for larger $n$ it may take a while.
I set the upper bound at $n=400$ to avoid freezing your browser.
Parameters: $1 + \frac{2}{\sqrt{N}}$ with probability $p_1$, and $1 - \frac{1}{\sqrt{N}}$ with probability $p_2$.
Models critical behavior near the uniform measure.
Parameter equals $v_1$ with probability $\frac{1}{\sqrt{N}}$, and $v_2$ with probability $\frac{\sqrt{N} - 1}{\sqrt{N}}$.
Models rare high-weight events in the limit.
Parameter equals $v_1$ with probability $\frac{1}{2}$, and $v_2$ with probability $\frac{1}{2}$.
Two-point discrete distribution.
Deterministic periodic pattern: $w_1, w_2, w_1, w_2, w_1, w_2, \ldots$
Fixed alternating weights with no randomness.
Parameters are independent and uniform on $[a,b]$.
Continuous uniform distribution.
Link to code
(This simulation is interactive, written in JavaScript, see the source code of this page at the link)
Link to code
(C++ code for the simulation)