Random Domino Tilings and the Arctic Circle Theorem

Details Random Domino Tilings and the Arctic Circle Theorem Random Domino Tilings and the Arctic Circle Theorem

1998-01-13

arxiv.org/abs/math/9801068v1

Mathematics

Combinatorics

37 pages of text plus 9 pages of figures (separate). [Note: This is not the final draft of this article.]

Scientific paper

In this article we study domino tilings of a family of finite regions called Aztec diamonds. Every such tiling determines a partition of the Aztec diamond into five sub-regions; in the four outer sub-regions, every tile lines up with nearby tiles, while in the fifth, central sub-region, differently-oriented tiles co-exist side by side. We show that when n is sufficiently large, the shape of the central sub-region becomes arbitrarily close to a perfect circle of radius n/sqrt(2) for all but a negligible proportion of the tilings. Our proof uses techniques from the theory of interacting particle systems. In particular, we prove and make use of a classification of the stationary behaviors of a totally asymmetric one-dimensional exclusion process in discrete time.

Affiliated with

Also associated with

No associations

Rating

Random Domino Tilings and the Arctic Circle Theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Random Domino Tilings and the Arctic Circle Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random Domino Tilings and the Arctic Circle Theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-644462