Unimodularity in Randomly Generated Graphs

This volume contains the proceedings of the AMS Special Session on Unimodularity in Randomly Generated Graphs, held from October 8-9, 2016, in Denver, Colorado. Unimodularity, a term initially used in locally compact topological groups, is one of the main examples in which the generalization from groups to graphs is successful. The ``randomly generated graphs'', which include percolation graphs, random Erdos-Renyi graphs, and graphings of equivalence relations, are much easier to describe if they result as random objects in the context of unimodularity, with respect to either a vertex-transient ``host''-graph or a probability measure. This volume tries to give an impression of the various fields in which the notion currently finds strong development and application: percolation theory, point processes, ergodic theory, and dynamical systems.