Oct 25, 2012 · 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})

Apr 29, 2014 · Intuitively, Theorem 4.1 implies that when there is replica symmetry, for large n, the random graph behaves like an Erdős-Rényi random graph (or ...

The following question was raised by Chatterjee and Varadhan [8] concerning large deviations in G(n, p), the Erd˝os-Rényi random graph on n vertices with edge ...

On replica symmetry of large deviations in random graphs. Authors: Eyal Lubetzky. Eyal Lubetzky. Theory Group of Microsoft Research, One Microsoft Way, Redmond ...

Aug 1, 2015 · Via a beautiful new framework for large deviation principles in G(n,p),Chatterjee and Varadhan gave bounds on the replica symmetric phase, the ...

Replica symmetry: If minimized (uniquely) by the constant graphon, then the conditioned random graph is close to Erdős–Rényi (in cut distance). Page 15. Sparse ...

Lubetzky, Y. Zhao. "On replica symmetry of large deviations in random graphs." Random Struct. Algor. 47:1 (2015): 109-146.

Feb 4, 2016 · As it turns out, however, the replica symmetric phase is strictly larger, being governed instead by x 7→ hp(. √ x). (See Fig. 1.) Page 3. ON ...

Large deviations for random graphs. Page 20. 'Replica symmetry breaking'. The following theorem shows that given any t, for all p small enough, the conditional ...

From the physical point of view, it is simply the effect of replica symmetry breaking down in the “low temperature regime”. ... The large deviation principle for ...