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Keyword: replica symmetry ×Clear all

1 claim from 1 paper

1. Mathematics › Limits and Structures in Graph Theory

   On replica symmetry of large deviations in random graphs

   Lubetzky and Zhao · Random Structures and Algorithms · 2014

   The paper identifies the replica symmetric phase for triangle counts and other fixed regular subgraphs in conditioned Erdős-Rényi random graphs, settling a question of Chatterjee and Varadhan.

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   1. UncheckedThe replica symmetric region is all (p,r) where the point (r^d, h_p(r)) lies on the convex minorant of x ↦ h_p(x^{1/d}), with h_p the binomial rate function.“By analyzing the variational problem arising from the framework of Chatterjee and Varadhan we show that the replica symmetry phase consists of all $(p,r)$ such that $(r^d,h_p(r))$ lies on the convex minorant of $x\mapsto h_p(x^{1/d})$ where $h_p$ is the rate function of a binomial with parameter $p…”