The arctic circle boundary and the Airy process

• 成果类型: Article
• 署名作者: Johansson, K
• 署名单位: Royal Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000937
• 发表日期: 2005
• 页码: 1-30
• 关键词: nonintersecting paths; local statistics; domino tilings; fluctuations

摘要

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.