Non-intersecting paths, random tilings and random matrices

• 成果类型: Article
• 署名作者: Johansson, K
• 署名单位: Royal Institute of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400100187
• 发表日期: 2002
• 页码: 225-280
• 关键词: domino tilings; Orthogonal polynomials; spacing distributions; local statistics; vicious walkers; rhombus tilings; LIMIT-THEOREMS; 6-vertex model; fixed rhombus; asymptotics

摘要

We investigate certain measures induced by families of non-intersecting paths in domino tilings of the Aztec diamond, rhombus tilings of an abc-hexagon, a dimer model on a cylindrical brick lattice and a growth model. The measures obtained, e.g. the Krawtchouk and Hahn ensembles, have the same structure as the eigenvalue measures in random matrix theory like GUE, which can in fact can be obtained from non-intersecting Brownian motions. The derivations of the measures are based on the Karlin-McGregor or Lindstrom-Gessel-Viennot method. We use the measures to show some asymptotic results for the models.