An $L^{p}$ theory of sparse graph convergence II: LD convergence, quotients and right convergence

Annals of Probability, pp. 337-396, 2018.

Cited by: 32|Bibtex|Views37|DOI:https://doi.org/10.1214/17-aop1187
Other Links: academic.microsoft.com|arxiv.org

Abstract:

We extend the $L^p$ theory of sparse graph limits, which was introduced in a companion paper, by analyzing different notions of convergence. Under suitable restrictions on node weights, we prove the equivalence of metric convergence, quotient convergence, microcanonical ground state energy convergence, microcanonical free energy converg...More

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