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Full Description
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.
Contents
R. Lyons, Monotonicity of average return probabilities for random walks in random environments
O. Angel and T. Hutchcroft, Counterexamples for percolation on unimodular random graphs
I. Benjamini and O. Gurel-Gurevich, Invariant $\rho$-percolation on regular trees
I. Benjamini and G. Elek, Sparse graph limits along balls
I. Benjamini, Percolation and coarse conformal uniformization
A. Timar, Invariant tilings and unimodular decorations of Cayley graphs
E. Paquette, Distributional lattices on Riemannian symmetric spaces
F. Baccelli, M.-O. Haji-Mirsadeghi, and A. Khezeli, Eternal Family Trees and dynamics on unimodular random graphs
V. A. Kaimanovich, Circular slider graphs: de Bruijn, Kautz, Rauzy, lamplighters and spiders
L. Bowen, All properly ergodic Markov chains over a free group are orbit equivalent
A. Khezeli, Shift-coupling of random rooted graphs and networks.
