Limits of discrete distributions and Gibbs measures on random graphs
arXiv:1512.06798 · doi:10.1016/j.ejc.2017.06.012
Abstract
Building upon the theory of graph limits and the Aldous-Hoover representation and inspired by Panchenko's work on asymptotic Gibbs measures (Annals of Probability 2013), we construct continuous embeddings of discrete probability distributions. We show that the theory of graph limits induces a meaningful notion of convergence and derive a corresponding version of the Szemerédi regularity lemma. Moreover, complementing recent work (Bapst et. al. 2015), we apply these results to Gibbs measures induced by sparse random factor graphs and verify the "replica symmetric solution" predicted in the physics literature under the assumption of non-reconstruction.
References in corpus (8)
- Gibbs States and the Set of Solutions of Random Constraint Satisfaction Problems
- Graph limits and exchangeable random graphs
- Hiding Quiet Solutions in Random Constraint Satisfaction Problems
- The condensation phase transition in random graph coloring
- Harnessing the Bethe free energy
- Limits of compact decorated graphs
- Multigraph limits, unbounded kernels, and Banach space decorated graphs
- Reconstruction/Non-reconstruction Thresholds for Colourings of General Galton-Watson Trees