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: Zoom

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’.

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