Unimodularity in Randomly Generated Graphs
About this Title
Florian Sobieczky, Software Competence Center Hagenberg, Hagenberg in Mühlkreis, Austria, Editor
Publication: Contemporary Mathematics
Publication Year: 2018; Volume 719
ISBNs: 978-1-4704-3914-9 (print); 978-1-4704-5017-5 (online)
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 Erdős–Rényi 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.
Graduate students and research mathematicians interested in ergodic theory, dynamical systems, random graphs and applications.
Table of Contents
- Russell Lyons – Monotonicity of average return probabilities for random walks in random environments
- Omer Angel and Tom Hutchcroft – Counterexamples for percolation on unimodular random graphs
- Itai Benjamini and Ori Gurel-Gurevich – Invariant $\rho $-percolation on regular trees
- Itai Benjamini and Gabor Elek – Sparse graph limits along balls
- Itai Benjamini – Percolation and coarse conformal uniformization
- Ádám Timár – Invariant tilings and unimodular decorations of Cayley graphs
- Elliot Paquette – Distributional lattices on Riemannian symmetric spaces
- Francois Baccelli, Mir-Omid Haji-Mirsadeghi and Ali Khezeli – Eternal Family Trees and dynamics on unimodular random graphs
- Vadim A. Kaimanovich – Circular slider graphs: de Bruijn, Kautz, Rauzy, lamplighters and spiders
- Lewis Bowen – All properly ergodic Markov chains over a free group are orbit equivalent
- Ali Khezeli – Shift-coupling of random rooted graphs and networks