# Tomas Berggren: Double integral formulas for periodic multi-level particle systems

Time: Tue 2018-04-17 15.15 - 16.15

Lecturer: Tomas Berggren

Location: Room F11, KTH

Abstract:
Recently, important progress has been made on the asymptotic behavior of certain periodic multi-level 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. I will discuss a simplification in the case of certain particle systems with infinite levels. In those cases, the integrand in the double integral formula can be expressed in terms of a matrix Wiener-Hopf factorization for an associated weight function. If there is time, I will mention the solution of the factorization problem for the $2\times 2$ periodic weighting of lozenge tilings in a hexagon.

2018-04-17T15:15 2018-04-17T16:15 Tomas Berggren: Double integral formulas for periodic multi-level particle systems Tomas Berggren: Double integral formulas for periodic multi-level particle systems
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