Dear Colleagues and Students,
You are cordially invited to the Analysis Seminar organized by the Department of Mathematics.
Speaker: Elnur Emrah (Carnegie Mellon University)
“Exactly-solvable exponential corner growth model with inhomogeneous parameters”
Abstract: The corner growth model with exponential weights is a much studied stochastic planar growth model in the Kardar-Parisi-Zhang universality class. The interest in the model stems in part from its exact-solvability and connections to fundamental interacting particle systems such as TASEP. In this talk, we consider an inhomogeneous generalization of the exponential CGM by allowing the means of the weights to be site-dependent. In this model, we study the competition interface (Ferrari and Pimentel, 2005), a notion of boundary that separates two growing planar regions that are in competition for sites. We observe that the inhomogeneity of the weights causes a sharp dichotomy in the asymptotics: A.s., either the competition interface has an asymptotic direction or it remains confined in a narrow strip of the quadrant with finite width. We discuss this result and its counterparts for the related notions of Busemann limits and second-class customers in a sequence of servers. This is an ongoing joint work with C. Janjigian and T. Seppalainen.
Date: Tuesday, December 25, 2018
Place: Mathematics Seminar Room, SA – 141