The Annals of Probability

The arctic circle boundary and the Airy process

Kurt Johansson

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Abstract

We prove that the, appropriately rescaled, boundary of the north polar region in the Aztec diamond converges to the Airy process. The proof uses certain determinantal point processes given by the extended Krawtchouk kernel. We also prove a version of Propp’s conjecture concerning the structure of the tiling at the center of the Aztec diamond.

Article information

Source
Ann. Probab., Volume 33, Number 1 (2005), 1-30.

Dates
First available in Project Euclid: 11 February 2005

Permanent link to this document
https://projecteuclid.org/euclid.aop/1108141718

Digital Object Identifier
doi:10.1214/009117904000000937

Mathematical Reviews number (MathSciNet)
MR2118857

Zentralblatt MATH identifier
1096.60039

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs 15A52

Keywords
Airy process determinantal process Dimer model random matrices random tiling

Citation

Johansson, Kurt. The arctic circle boundary and the Airy process. Ann. Probab. 33 (2005), no. 1, 1--30. doi:10.1214/009117904000000937. https://projecteuclid.org/euclid.aop/1108141718


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