Karl Liechty

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Abstract. We consider the large-N asymptotics of a system of discrete orthogonal polynomials on an infinite regular lattice of mesh 1 N , with weight e , where V (x) is a real analytic function with sufficient growth at infinity. The proof is based on formulation of an interpolation problem for discrete orthogonal polynomials, which can be converted to a(More)
We obtain the large-n asymptotics of the partition function Zn of the six-vertex model with domain wall boundary conditions in the antiferroelectric phase region, with the weights a D sinh. t/, b D sinh. C t/, c D sinh.2 /, jt j < . We prove the conjecture of Zinn-Justin, that as n ! 1, Zn D C#4.n!/F n Œ1 C O.n 1/ , where ! and F are given by explicit(More)
with θ > 1. I will show that the biorthogonal polynomials associated to such models satisfy a recurrence relation and a Christoffel-Darboux formula if θ is rational, and that they can be characterized in terms of non-standard 1 × 2 Riemann-Hilbert problems. If w(λ) = e−nV , I will also construct the equilibrium measure associated to the model in the one-cut(More)
Abstract. This is a continuation of the papers [4] of Bleher and Fokin and [6] of Bleher and Liechty, in which the large n asymptotics is obtained for the partition function Zn of the six-vertex model with domain wall boundary conditions in the disordered and ferroelectric phases, respectively. In the present paper we obtain the large n asymptotics of Zn on(More)
This is a continuation of the paper [4] of Bleher and Fokin, in which the large n asymptotics is obtained for the partition function Zn of the six-vertex model with domain wall boundary conditions in the disordered phase. In the present paper we obtain the large n asymptotics of Zn in the ferroelectric phase. We prove that for any ε > 0, as n → ∞, Zn = CG(More)
We consider two Lax systems for the homogeneous Painlevé II equation: one of size 2×2 studied by Flaschka and Newell in the early 1980s, and one of size 4×4 introduced by Delvaux, Kuijlaars, and Zhang and Duits and Geudens in the early 2010s. We prove that solutions to the 4×4 system can be derived from those to the 2 × 2 system via an integral transform,(More)
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