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Softcover ISBN:  9781470439149 
Product Code:  CONM/719 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
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Product Code:  CONM/719.E 
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AMS Member Price:  $100.00 
Softcover ISBN:  9781470439149 
eBook ISBN:  9781470450175 
Product Code:  CONM/719.B 
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Book DetailsContemporary MathematicsVolume: 719; 2018; 211 ppMSC: Primary 60; 37
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 vertextransient “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.
ReadershipGraduate students and research mathematicians interested in ergodic theory, dynamical systems, random graphs and applications.

Table of Contents

Articles

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 GurelGurevich — 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, MirOmid HajiMirsadeghi 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 — Shiftcoupling of random rooted graphs and networks


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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 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 vertextransient “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.

Articles

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 GurelGurevich — 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, MirOmid HajiMirsadeghi 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 — Shiftcoupling of random rooted graphs and networks