Abstract
The talk will first introduce unimodular random graphs and give several examples from the theory of point processes, branching processes, random walks and self-similar discrete random sets. Several types of results on these graphs will then be reviewed :
- Unimodular extensions of classical theorems from Palm calculus and ergodic theory.
- A classification of deterministic or random dynamics on such graphs based on the properties of their stable varieties.
- Two new dimensional notions for such graphs, namely their unimodular Minkowski and Hausdorff dimensions.
This talk is based on a series of articles in collaboration with M.-O. Haji-Mirsadeghi and A. Khezeli.
