Persi Diaconis, Professor of Statistics and Mathematics at Stanford University, will give a lecture about « Adding numbers and shuffling cards ».
This lecture is part of the « Multiplicities » initiative launched by the Department of Mathematics at the University of Luxembourg. Multiplicities is a broad audience seminar geared towards transversal topics whose aim is to highlight the diversity of mathematics and mathematicians. It is especially intended for PhD students, interested in widening their horizons and is supported by the PRIDE Grant “Geometry, Probability and their Synergies (GPS)”.
About the topic
When numbers are added in the usual way, « carries » appear along the way. If you are me (and hopefully you after this talk) it’s natural to ask: « How do the carries go? How many are there and, if you just had a carry, is it more or less likely that the next sum has a carry? » Strangely, carries form a Markov chain with an « amazing » transition matrix. More strangely, this same matrix appears in the analysis of the usual way of riffle shuffling cards. I will explain the connection, tell you about the « seven shuffles theorem » and attempt to do it « in English ».
About the speaker
Persi Diaconis is a mathematician, statistician and former professional magician working in probability, combinatorics, and group theory with a focus on applications to statistics and scientific computing. He is particularly well known for studying the mathematics of randomness.