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Probability and Computational Finance Seminar
Sevak Mkrtchyan
Carnegie Mellon University
Title: The bulk scaling limit of unbounded plane partitions

Abstract: The dimer model is the study of random perfect matchings on graphs, and has a long history in statistical mechanics. On the hexagonal lattice it is equivalent to tilings of the plane by lozenges, which under certain boundary conditions correspond to 3D stepped surfaces called plane partitions. We will discuss the scaling limit of random plane partitions under the "uniform" measure. The model exhibits the phase transition phenomenon: at a certain scale it separates into regions with different nature of fluctuations. We will introduce the model in detail, discuss the methods used to compute the n-point correlation functions and study their scaling limit in the bulk (the "liquid" phase) using the saddle point method. The talk will be mostly expository based on the work of Okounkov and Reshetikhin.

Date: Monday, March 24, 2014
Time: 5:00 pm
Location: Wean Hall 8427
Submitted by:  Dmitry Kramkov