Rank Dynamics

Abstract: Almost anything can be ranked: people, teams, institutions, products, words, genes, etc. Rank distributions have been studied extensively: some have scale-free-like distributions, some do not. However, only recently we had enough data to study how rankings change in time. I will present an overview of our work where we have proposed a host of measures to analyze rank dynamics, and a basic model that can reproduce their regularities. We have found that in spite of having different mechanisms generating rank dynamics, these can be explained within the same framework, that can also be described in terms of balance.