Timeline for "Coarse" Arctic Circle Theorem
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Oct 5, 2021 at 5:17 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
fixed arxiv front-end link and gave titles
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| Apr 8, 2017 at 13:04 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Image link broken; now fixed.
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| Oct 18, 2011 at 19:32 | comment | added | Joseph O'Rourke | @Henry: I took the liberty of adding Fig.4 to your post. | |
| Oct 18, 2011 at 19:30 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Added Fig.4
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| Oct 18, 2011 at 16:26 | comment | added | Johan Wästlund | And to see what the height function is, we just chess-board color the region and walk around the boundary, keeping track of the difference in the number of black and white pieces of boundary we have seen. For the coarse aztec diamond this difference is bounded, so the height function is essentially constant. In contrast, for the ordinary aztec diamond, two sides are entirely black and two sides entirely white. | |
| Oct 18, 2011 at 16:23 | comment | added | Johan Wästlund | The "highest possible entropy at every point" means that the logarithm of the number of tilings of the coarse aztec diamond (just as for a square of even side or a region with "soft" boundary conditions) is asymptotically the area times $C/\pi$, where $C = 1-1/9+1/25-\dots$ is Catalan's constant, right? | |
| Oct 18, 2011 at 16:08 | history | edited | Henry Cohn | CC BY-SA 3.0 |
added 20 characters in body
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| Oct 18, 2011 at 16:04 | comment | added | David E Speyer | Henry: You should probably clarify a point, unless I am mistaken: The Kenyon-Okounkov solution applies to the rhombus tiling situation, and I don't think KO have published how to modify it for domino tilings. Other than that, nice answer! | |
| Oct 18, 2011 at 15:55 | history | answered | Henry Cohn | CC BY-SA 3.0 |