Biostatistics Seminar: Ian McKeague

Presentation: Free Multiplicative Cascades and Wigner’s Semicircle Law

Speaker: Ian McKeague, Ph.D., Professor of Biostatistics, Columbia Mailman School of Public Health

Abstract: It has been conjectured that phenomena as diverse as the behavior of large “self-organizing” neural networks, and causality in standard model particle physics, can be explained by suitably rich algebras acting on themselves. In this talk I discuss the asymptotics of large causal tree diagrams that combine freely independent elements of such algebras. The Marchenko-Pastur law and Wigner’s semicircle law are shown to emerge as limits of a normalized sum-over-paths of non-negative elements assigned to the edges of causal trees. The results are established in the setting of non-commutative probability. Trees with classically independent positive edge weights (random multiplicative cascades) were originally proposed by Mandelbrot as a model displaying the fractal features of turbulence. The novelty of the present work is the use of non-commutative (free) probability to allow the edge weights to take values in an algebra.

Thu, Mar 8, 2018, 3:30pm to 5:00pm
Room T-639 (HST)

Faculty Coordinator: Amy Willis,

Seminar Coordinator: Sandra Coke,