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

  title={An \$L^\{p\}\$ theory of sparse graph convergence II: LD convergence, quotients and right convergence},
  author={Christian Borgs and Jennifer T. Chayes and Henry Cohn and Yufei Zhao},
  journal={Annals of Probability},
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… 

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