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Probability and Computational Finance Seminar
Elnur Emrah
Carnegie Mellon University
Title: Fluctuations and large deviations exactly solvable inhomogeneous corner growth models

Abstract: The conjectural Kardar-Parisi-Zhang (KPZ) universality class includes a diverse variety of models of interface growth, percolation, polymers and single-lane traffic. A characteristic feature of KPZ class models is that the quantities of interest, such as the interface height, the weight of the optimal path, the partition function and particle current, share the same asymptotic properties; as the system size $n$ tends to infinity, fluctuations grow in the order of $n^{1/3}$, nontrivial spatial correlations occur at scale $n^{2/3}$ and limit distributions are Tracy-Widom distributions. At present, these properties can be verified with mathematical rigor only for exactly solvable models which permit precise analysis due to additional algebraic/combinatorial structure. The corner growth model describes a randomly growing cluster in a quadrant of the plane. It is one of the earliest models discovered to be exactly solvable and proved to lie in KPZ class. In this talk, we generalize the corner growth model with geometric weights by allowing weight parameters to be inhomogeneous and randomly chosen from an ergodic distribution. We show that, conditioned on the parameters, last-passage time variables exhibit KPZ statistics as in the homogeneous case but only in a certain cone in the quadrant determined by the distribution of the parameters.

Date: Monday, October 17, 2016
Time: 4:30 pm
Location: Wean Hall 8220
Submitted by:  Steve Shreve