INVARIANT MEASURES CONCENTRATED ON COUNTABLE STRUCTURES

DOI10.1017/fms.2016.15OpenAlexW3100613408MaRDI QIDQ5739903

Rehana Patel, Cameron E. Freer, Nathanael Leedom Ackerman

Publication date: 6 July 2016

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.4011

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Characterization and structure theory of statistical distributions (62E10) Applications of model theory (03C98) Other infinitary logic (03C75) Exchangeability for stochastic processes (60G09) Infinite graphs (05C63) Invariant measures for infinite-dimensional dissipative dynamical systems (37L40)

Related Items

A classification of orbits admitting a unique invariant measure, RELATIVELY EXCHANGEABLE STRUCTURES, Bowtie-free graphs have a Ramsey lift, Invariant measures via inverse limits of finite structures, Positive families and Boolean chains of copies of ultrahomogeneous structures, Semantic limits of dense combinatorial objects, HENKIN CONSTRUCTIONS OF MODELS WITH SIZE CONTINUUM, Relational exchangeability, A generalization of hierarchical exchangeability on trees to directed acyclic graphs, Cohen-like first order structures, Simple structures axiomatized by almost sure theories

Cites Work

• Properties of the automorphism group and a probabilistic construction of a class of countable labeled structures
• Limits of dense graph sequences
• Invariant measures via inverse limits of finite structures
• Generic separable metric structures
• On exchangeable random variables and the statistics of large graphs and hypergraphs
• Complexity ranks of countable models
• Quasi finitely axiomatizable totally categorical theories
• Countable homogeneous partially ordered sets
• Representations for partially exchangeable arrays of random variables
• Symmetries on random arrays and set-indexed processes
• Universal graphs with forbidden subgraphs and algebraic closure
• Multivariate sampling and the estimation problem for exchangeable arrays
• On random relational structures
• Limits of permutation sequences
• A survey of homogeneous structures
• Poset limits and exchangeable random posets
• Some isometry groups of the Urysohn space
• Concerning measures in first order calculi
• Model theory for infinitary logic. Logic with countable conjunctions and finite quantifiers
• Random graphons and a weak Positivstellensatz for graphs
• Uncountable graphs and invariant measures on the set of universal countable graphs
• Probability with Martingales
• The classification of countable homogeneous directed graphs and countable homogeneous 𝑛-tournaments
• Barwise: Infinitary Logic and Admissible Sets
• Universal graphs with a forbidden near‐path or 2‐bouquet
• Flag algebras
• Random Graphs
• Representation of symmetric probability models
• Countable homogeneous relational structures and ℵ₀-categorical theories
• Probabilistic Symmetries and Invariance Principles
• Some remarks on universal graphs