Marked GUE-corners processes and periodically weighted Aztec diamonds
A talk in the Seminar Zufallsmatrizen series by
Nedialko Bradinoff
| Abstract: | The Aztec diamond dimer model is classical in statistical mechanics. The Aztec diamond with uniform weights, for its remarkable and special structure, has been a guiding object in establishing a set of remarkable local and global results in the limit as the size of the model tends to infinity. In recent years new tools were developed and made it possible to also study the Aztec diamond with doubly periodic weights and, in great generality, at the global and local scales new limiting phenomena were proved. In this talk I will discuss a new local limit for the Aztec diamond for a family of $2\times \ell$ periodic weights. We study an interlacing particle system near one of the points where the liquid disordered region touches the boundary. At this $\textit{turning}$ point under an appropriate scaling we observe a marked GUE-corners process as the size of the model grows. This is a determinantal point process obtained from the celebrated GUE-corners process by assigning independent Bernoulli marks (with location-dependent parameters) to each particle in a configuration. The Bernoulli parameters reflect the periodic weights. The proof relies on a double-contour integral representation over a certain Riemann surface of the correlation kernel of the studied process. The talk is based on joint work with Tomas Berggren. Within the CRC this talk is associated to the project(s): C6 |