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Probability and Computational Finance Seminar
Sevak Mkrtchyan
Carnegie Mellon University
Title: Plane partitions with 2-periodic weights

Abstract: We will discuss scaling limits of skew plane partitions with periodic weights under several boundary conditions and study differences with the case of homogeneous weights. We compute the correlation kernel of the limiting point process in the bulk and near turning points on the frozen boundary. The turning points that appear in the homogeneous case split in our model into pairs of turning points macroscopically separated by a ``semi-frozen'' region. As a result the point process at a turning point is not the GUE minor process, but rather a pair of GUE minor processes, non-trivially correlated.

We also study an intermediate regime when the weights are periodic but all converge to $1$. In this regime the limit shape and correlations in the bulk are the same as in the case of homogeneous weights and periodicity is not visible in the bulk. However the process at turning points is still not the GUE minor process.

Date: Monday, October 21, 2013
Time: 5:00 pm
Location: Wean Hall 6423
Submitted by:  Dmitry Kramkov