#### Filter Results:

- Full text PDF available (6)

#### Publication Year

2007

2016

- This year (0)
- Last 5 years (2)
- Last 10 years (6)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- Pavel Bleher, Karl Liechty
- 2009

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)

- Pavel Bleher, Karl Liechty
- 2009

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)

- Pavel Bleher, Vladimir Fokin, +6 authors Pavel Bleher
- 2014

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)

- Pavel Bleher, Karl Liechty
- 2008

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)

- Pavel Bleher, Karl Liechty
- 2007

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)

- Karl Liechty, Dong Wang
- SIAM J. Math. Analysis
- 2016

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)

- ‹
- 1
- ›