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Probability and Computational Finance Seminar
Mark Cerenzia
Title: Local limit behavior and Gaussian fluctuations of Plancherel growth processes

Abstract: Plancherel growth processes are certain continuous dynamics for (Gelfand-Tsetlin) point patterns that serve as prototypes for studying universality phenomena in 2 space + 1 time dimensions. Our talk will investigate the sensitivity of the items in the title to boundary conditions and to (global) deformation. Toward this end, we first review how these point processes in the plane are projections of classical representation theoretic objects, leading to an explicit determinantal description of their correlation structure. This allows us to discuss how boundary conditions (reflection vs. absorption) can influence local limit behavior. We next turn our attention to recent literature that realizes a growth process as the restriction of a noncommutative random walk. On-going work (joint with Jeffrey Kuan) studies the multipoint fluctuations of the height function in an analogous model of random growth. We observe how a deformation of the system leads to a Gaussian field that agrees with the undeformed case along certain paths ("space-like") but disagrees along others ("time-like").

Date: Monday, November 16, 2015
Time: 4:30 pm
Location: Wean Hall 8220
Submitted by:  Kasper Larsen