Local statistics for random domino tilings of the Aztec diamond

• Main Authors: Cohn, Henry, Elkies, Noam, Propp, James
• Format: Text
• Language: unknown
• Published: arXiv 2000
• Subjects: Combinatorics math.CO; Probability math.PR; FOS Mathematics; Primary 60K35, 82B20, Secondary 05A16, 60C05; Arctic; Saddle Point
• Online Access: https://dx.doi.org/10.48550/arxiv.math/0008243; https://arxiv.org/abs/math/0008243

We prove an asymptotic formula for the probability that, if one chooses a domino tiling of a large Aztec diamond at random according to the uniform distribution on such tilings, the tiling will contain a domino covering a given pair of adjacent lattice squares. This formula quantifies the effect of...