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Exact solutions to the six-vertex model with domain wall boundary conditions
Probability| Speaker: | Karl kliechty, IUPUI |
| Location: | 3106 MSB |
| Start time: | Wed, Dec 1 2010, 4:10PM |
Description
The six vertex model is a two dimensional model of statistical mechanics
realized on an $n \times n$ square lattice. In this talk, we consider
specific fixed boundary conditions on this model known as domain wall
boundary conditions (DWBC). With these boundary conditions, states of the
six-vertex model are in bijection with the set of $n \times n$ alternating
sign matrices. A very nice determinantal formula for the partition
function
of the six-vertex model with DWBC was derived by Izergin and Korepin in
the 1980's. About 10 years ago, Paul Zinn-Justin noticed that the
Izergin-Korepin formula can be written in the form of the partition
function for a random matrix-type ensemble, making it amenable to
asymptotic analysis. In this talk, I will discuss the Izergin-Korepin
formula, the random matrix interpretation, and the asymptotic analysis,
which is based on the Riemann-Hilbert approach.