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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.
Florian Sobieczky, Software Competence Center Hagenberg, Hagenberg in Muhlkreis, Austria.
R. Lyons, Monotonicity of average return probabilities for random walks in random environmentsO. Angel and T. Hutchcroft, Counterexamples for percolation on unimodular random graphsI. Benjamini and O. Gurel-Gurevich, Invariant $\rho$-percolation on regular treesI. Benjamini and G. Elek, Sparse graph limits along ballsI. Benjamini, Percolation and coarse conformal uniformizationA. Timar, Invariant tilings and unimodular decorations of Cayley graphsE. Paquette, Distributional lattices on Riemannian symmetric spacesF. Baccelli, M.-O. Haji-Mirsadeghi, and A. Khezeli, Eternal Family Trees and dynamics on unimodular random graphsV. A. Kaimanovich, Circular slider graphs: de Bruijn, Kautz, Rauzy, lamplighters and spidersL. Bowen, All properly ergodic Markov chains over a free group are orbit equivalentA. Khezeli, Shift-coupling of random rooted graphs and networks.
Gabriele Kotsis, A Min Tjoa, Ismail Khalil, Bernhard Moser, Atif Mashkoor, Johannes Sametinger, Anna Fensel, Jorge Martinez-Gil, Lukas Fischer, Gerald Czech, Florian Sobieczky, Sohail Khan
Gabriele Kotsis, A Min Tjoa, Ismail Khalil, Bernhard Moser, Alfred Taudes, Atif Mashkoor, Johannes Sametinger, Jorge Martinez-Gil, Florian Sobieczky, Lukas Fischer, Rudolf Ramler, Maqbool Khan, Gerald Czech