Adding Numbers and Shuffling Cards

Professor Persi Diaconis

Stanford University
Barton Lectures in Computational Mathematics


Date: Wednesday, September 9, 2020
Time: 4:00 pm - 5:00 pm
Location: Virtual through Zoom
Dr. Persi Diaconis is a mathematician and statistician working in probability, combinatorics, and group theory with a focus on applications to statistics and scientific computing. One of his specialties is rates of convergence of Markov chains. He is currently interested in trying to adapt the many mathematical developments to say something useful to practitioners in large real-world simulations. He is a member of the National Academy of Sciences and the American Philosophical Society, and a Fellow of the American Academy of Arts and Sciences, American Statistical Association and the Institute of Mathematical Statistics.

Abstract: When numbers are added in the usual way, ‘carries’ occur along the way. It is natural to ask ‘for typical numbers, how do the carries go?’ It turns out that the carries form a Markov chain with an ‘AMAZING’ transition matrix. This same matrix occurs in analyzing the usual riffle  shuffle we use when mixing cards. The matrix also occurs in taking sections of generating functions and in the fractal analysis of Pascal’s triangle. The different appearances interact and remind us that different areas of mathematics all connect.  I will explain all of this ‘in English’.