Persi Diaconis - “Adding Numbers and Shuffling Cards”

Stanford University
APPLIED PHYSICS/PHYSICS COLLOQUIUM
Please note: Paul Kirkpatrick Awards will be announced at this colloquium

Tuesday, February 5, 2019
4:30 p.m. on campus in Hewlett Teaching Center, Rm. 201
Persi Diaconis
Stanford University, Dept. of Statistics and Mathematics

“Adding Numbers and Shuffling Cards”

Just like you folks, (some) mathematicians look at the world and try to make sense of it. For example, when numbers are added in the usual way, ‘carries’ occur. It is natural to ask “how do the carries go?” How many carries are typical, and if we just had a carry, is it more (or less) likely that the next column will need a carry? It turns out that carries form a Markov chain with an “amazing” Transition matrix. Surprisingly, this same matrix turns up in the analysis of shuffling cards (the “seven shuffles theorem”). I will explain the connection and links to all kinds of other parts of mathematics: for example, sections of generating functions, the Veronese imbedding, Foulkes characters and Hopf algebras. The results “deform” and that is important in the analysis of casino “shelf shuffling machines.”