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January 2005 The arctic circle boundary and the Airy process
Kurt Johansson
Ann. Probab. 33(1): 1-30 (January 2005). DOI: 10.1214/009117904000000937

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.

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Kurt Johansson. "The arctic circle boundary and the Airy process." Ann. Probab. 33 (1) 1 - 30, January 2005. https://doi.org/10.1214/009117904000000937

Information

Published: January 2005
First available in Project Euclid: 11 February 2005

zbMATH: 1096.60039
MathSciNet: MR2118857
Digital Object Identifier: 10.1214/009117904000000937

Subjects:
Primary: 60K35
Secondary: 15A52 , 82B20

Keywords: Airy process , Determinantal process , Dimer model , random matrices , random tiling

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 1 • January 2005
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