Explore a 48-minute lecture on the Radon-Nikodym topography of amenable equivalence relations in acyclic graphs, presented by Robin Tucker-Drob from the University of Florida at IPAM's Statistical Mechanics Beyond 2D Workshop. Delve into Adams' dichotomy for ergodic acyclic graphs in measure-preserving settings and its extension to measure-class-preserving scenarios. Discover how the concept of "non-vanishing ends" is used to adapt the dichotomy, and understand the connection between local component behavior of the Radon-Nikodym cocycle and global properties like amenability through tools such as mass-transport. Gain insights into the geometric interpretation of Radon-Nikodym cocycles within graphs and their implications for statistical mechanics beyond two dimensions.