Asymptotic Geometry of Discrete Interlaced Patterns: Part II

2015/07/02 by Duse, Erik, Metcalfe, Anthony
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1507.00467

Abstract

We study the boundary of the liquid region L in large random lozenge tiling models defined by uniform random interlacing particle systems with general initial configuration, which lies on the line (x,1), x∈ℝ≡ ∂ ℍ. We assume that the initial particle configuration converges weakly to a limiting density ϕ(x), 0≤ ϕ≤ 1. The liquid region is given by a homeomorphism W_L: L→ ℍ, the upper half plane, and we consider the extension of W_L^-1 to ℍ. Part of ∂ L is given by a curve, the edge E, parametrized by intervals in ∂ ℍ, and this corresponds to points where ϕ is identical to 0 or 1. If 0

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