Probability and Computational Finance Seminar

Sevak Mkrtchyan
Carnegie Mellon University
Title: Random Skew Plane Partitions with Arbitrary Piecewise Linear Back Walls

Abstract: We study random skew plane partitions confined to a finite region, but with unbounded height, when the boundary of the inner shape consists of a piecewise linear function of slopes in [-1,1]. The system is equivalent to perfect matchings on the hexagonal lattice with certain boundary conditions, or to tilings of the plane by three types of rhombi. We show that in the scaling limit frozen and liquid regions appear, and we study the frozen boundary and local fluctuations. In the bulk and at the frozen boundary we observe the same point processes as obtained by Okounkov and Reshetikhin in the case when the slopes are only 1 and -1; the processes are the incomplete beta and Airy processes respectively. However, we observe a new behavior high up on the wall. We relate this system to the bead process introduced by Boutiller, and observe a new point process appearing near a certain "asymptotic turning point".

Date: Monday, October 15, 2012
Time: 5:00 pm
Location: Wean Hall 6423
Submitted by:  Pisztora