Decomposable random combinatorial structures
How do agents cluster or form subgroups in a market? What are the distributions of fractions on (high-dimensional) simplexes? These questions essentially have to do with random combinatorial structures such as random partitions.
We borrow from Watterson (1976), Watterson and Guess (1977), and, more recently, Arratia (1992) and others to deal with the questions of multiplicities of microeconomic states compatible with a set of observations of (macroeconomic or mesoscopic) variables. In the second longest chapter of this book, Chapter 10, we connect three types of transition rates with three types of distributions, and discuss dynamics of clusters. Some of the results are then applied in Chapter 11, in which the two largest groups are on the opposite sides of the market and their excess demands drive the price dynamics of the shares.1.6