Double integral formulas for certain doubly periodic point process

by Tomas Berggren (KTH Royal Institute of Technology)

Location: 200B.02.18, Leuven
Time: Thursday December 6, 2018 at 15:15

Recently, important progress has been made on the asymptotic behavior of certain doubly periodic particle systems, such as the periodic weightings of domino tilings of the Aztec diamond and periodic weightings of lozenge tilings of a hexagon. In a general setting Duits and Kuijlaars recently proved a double integral formula for the kernel of the point process in terms of matrix valued orthogonal polynomials. This result is an important step, since an explicit double integral formula for the kernel is a good starting point for asymptotic analysis.

I will discuss domino tilings of the Aztec diamond, and in particular give an explicit double integral formula for the kernel of models with multiple gas phases. I will discuss the proof, which is build on the double integral formula given by Duits and Kuijlaars, and that we have a matrix Wiener-Hopf factorization for an associated weight function.