All Questions
Tagged with pr.probability tiling
7 questions
5
votes
2
answers
323
views
Distribution over Penrose Tilings?
The set of possible kit-and-dart Penrose tilings is uncountably infinite. It would be very helpful to have some natural probability distribution $\mu$ over this set; such a distribution would allow ...
- 3,979
11
votes
1
answer
392
views
Growing a chain of unit-area triangles: Fills the plane?
Define a process to start with a unit-area equilateral triangle,
and at each step glue on another unit-area triangle.
$50$ ...
- 151k
4
votes
0
answers
152
views
Mixing time for dimers on the square-octagon graph
Consider the "fortress graph" of order $n$ (see Figure 9 of http://faculty.uml.edu/jpropp/tiling/www/mdblum/arctic.html). It's been known empirically for twenty years that if one turns the set of ...
- 19.7k
2
votes
0
answers
143
views
Arctic Circle Theorems and the Wave Equation
I've seen the following remark in a number of papers but don't know what to make of it. In this paper by Cohn, Elkies and Propp, it is mentioned that the normalized average Height function $\mathcal{H}...
- 4,952
3
votes
1
answer
179
views
Domino Shuffling and Warren's process
In this paper by Nordenstam, it is shown that a certain interlacing particle process that arises from uniformly random Aztec diamond tilings is amazingly similar to Warren's process. One of the ...
- 4,952
4
votes
0
answers
117
views
symmetric difference of temperate zone and inscribed disk
For random domino tilings of the Aztec diamond of order $n$ or random lozenge tilings of the regular hexagon of order $n$, what's the typical order of magnitude of the area of the symmetric difference ...
- 19.7k
9
votes
1
answer
394
views
computing average height-functions for lozenge tilings
Can anyone suggest a simple and efficient way (preferably embodied in computer code) to compute the average height function for lozenge tilings of an $a,b,c,a,b,c$ semiregular hexagon? I prefer to ...
- 19.7k