Random walks on the STOMACH graph.
Suppose we start at a tiling, say, the one on the right.
At each step, we flip a coin and with equal probability
choose
an adjacent tiling one move away.
How many steps does it take to reach a "random" tiling?
We have computed the eigenvalues of the Laplacian of the STOMACH graph
which can help solve this problem.
The spectral gap is 0.02573644110. This implies that in roughly 39 (~ 1/0.02578...) moves to reach a "random" tiling.
More to come.