Introduction

We consider a network of n agents, that update their opinions based on those of their neighbors in the network. Some of these models are also used to study the spread of epidemics. We note that this is mathematics course, analyzing mathematical models and not data. Models studied include the classical voter model, dual to coalescing random walks, majority dynamics, averaging dynamics, granular averaging, and others. There will be no final exam, but each student will be expected to take careful notes during one lecture.

Video Public: Yes

Notes Public: Yes

Audience: Graduate

Language: English

About the speaker

Yuval Peres obtained his PhD in 1990 from the Hebrew University, Jerusalem. He was a postdoctoral fellow at Stanford and Yale, and was then a Professor of Mathematics and Statistics in Jerusalem and in Berkeley. Later, he was a Principal researcher at Microsoft. Yuval has published more than 350 papers in most areas of probability theory, including random walks, Brownian motion, percolation, and random graphs. He has co-authored books on Markov chains, probability on graphs, game theory and Brownian motion, which can be found at https://www.yuval-peres-books.com. His presentations are available at https://yuval-peres-presentations.com.

Dr. Peres is a recipient of the Rollo Davidson prize and the Loeve prize. He has mentored 21 PhD students including Elchanan Mossel (MIT, AMS fellow), Jian Ding (PKU, ICCM gold medal and Rollo Davidson prize), Balint Virag and Gabor Pete (Rollo Davidson prize).

Dr. Peres was an invited speaker at the 2002 International Congress of Mathematicians in Beijing, at the 2008 European congress of Math, and at the 2017 Math Congress of the Americas. In 2016, he was elected to the US National Academy of Science.