Random tilings and matrix valued orthogonal polynomials

The aim of this research project is to study random tilings of planar domains with very special properties.
The tiling problems we have in mind have a rich combinatorial structure which allows for explicit formulas of relevant probabilistic quantities.
The expicit formulas are in many cases tractable to asymptotic analysis when the system size tends to infinity.

In recent work a specific model called the two-periodic Aztec diamond has been analyzed in great detail with the use of matrix valued orthogonal polynomials.
Three different phases were found In the large size limit of this two-periodic Aztec diamond, namely a solid, liquid and gas phase.
The gas phase is of special interest as it is  due to the periodicity in the model.

We want to apply the new method of matrix valued orthogonal polynomials to other random tiling models where we hope to 
discover the  gas phase and describe it in as much detail as possible.