An $L^{p}$ theory of sparse graph convergence II: LD convergence, quotients and right convergence
By Christian Borgs, Jennifer Tour Chayes, Henry Cohn, Yufei Zhao. 2014
98 citations recorded by the source corpus.
We extend the LpLp 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 convergence and large deviation convergence. Our theorems extend the broad applicability of dense graph convergence to all sparse graphs with unbounded average degree, while the proofs require new techniques based on uniform upper regularity. Examples to which our theory applies include stochastic block models, power law graphs and sparse versions of WW-random graphs.
Subfields: Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/36e3cf186ebc510800fb6e217cc8edae93fbf4f9
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In Mathematical Physics
Citations in the corpus
- Action convergence of operators and graphs (2018, background): “In the first part of this section, we relate P -operator convergence to the so-called quotient convergence, which was studied in different forms by different authors [8, 11, 26].”