Ultraproducts of measure preserving actions and graph combinatorics

DOI10.1017/S0143385711001143zbMath1268.05104OpenAlexW2082843053MaRDI QIDQ4928730

Clinton T. Conley, Alexander S. Kechris, Robin D. Tucker-Drob

Publication date: 18 June 2013

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385711001143

zbMATH Keywords

infinite countable groupsgraph combinatoricsgraphs associated to measure-preserving actionsultraproduct constructions

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Other combinatorial set theory (03E05)

Related Items (17)

Approximate Schreier decorations and approximate Kőnig's line coloring theorem ⋮ Weak containment rigidity for distal actions ⋮ On sofic groupoids and their full groups ⋮ An uncountable ergodic Roth theorem and applications ⋮ Borel fractional colorings of Schreier graphs ⋮ The space of stable weak equivalence classes of measure-preserving actions ⋮ Approximate equivalence of group actions ⋮ BROOKS’ THEOREM FOR MEASURABLE COLORINGS ⋮ Weak equivalence and non-classifiability of measure preserving actions ⋮ Topology and convexity in the space of actions modulo weak equivalence ⋮ A determinacy approach to Borel combinatorics ⋮ Weak density of orbit equivalence classes of free group actions ⋮ Weak containment of measure-preserving group actions ⋮ Characters of inductive limits of finite alternating groups ⋮ EXISTENCE OF MODELING LIMITS FOR SEQUENCES OF SPARSE STRUCTURES ⋮ Non-standard limits of graphs and some orbit equivalence invariants ⋮ Global aspects of measure preserving equivalence relations and graphs

Cites Work

• Perfect matchings as IID factors on non-amenable groups
• Entropy and isomorphism theorems for actions of amenable groups
• A simple proof of the ergodic theorem using nonstandard analysis
• Borel chromatic numbers
• Kazhdan's property T and the geometry of the collection of invariant measures
• Topics in orbit equivalence
• Processes on unimodular random networks
• Amenable actions of locally compact groups
• Moyennes invariantes et représentations unitaires
• Borel oracles. An analytical approach to constant-time algorithms
• Hyperlinear and Sofic Groups: A Brief Guide
• Ergodic Theory

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