What is the probability we have exactly one loop of thread, and what is the expected number of loops?
I had the same thought. I expect the probability of one loop trivially goes to zero as the tiling goes to infinity—because of the small loops—and that a better question would be whether there is an infinite loop. That looks an interesting (and hard!) percolation problem.
I had the same thought. I expect the probability of one loop trivially goes to zero as the tiling goes to infinity—because of the small loops—and that a better question would be whether there is an infinite loop. That looks an interesting (and hard!) percolation problem.