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- W2897314826 abstract "In [18] we analysed a simple undirected random graph subject to constraints on the total number of edges and the total number of triangles. We considered the dense regime in which the number of edges per vertex is proportional to the number of vertices. We showed that, as soon as the constraints are emph{frustrated}, i.e., do not lie on the Erdős-Renyi line, there is breaking of ensemble equivalence, in the sense that the specific relative entropy per edge of the emph{microcanonical ensemble} with respect to the emph{canonical ensemble} is strictly positive in the limit as the number of vertices tends to infinity. In the present paper we analyse what happens near the Erdős-Renyi line. It turns out that the way in which the specific relative entropy tends to zero depends on whether the total number of triangles is slightly larger or slightly smaller than typical. We investigate what the constrained random graph looks like asymptotically in the microcanonical ensemble." @default.
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- W2897314826 date "2018-07-20" @default.
- W2897314826 modified "2023-09-22" @default.
- W2897314826 title "Breaking of ensemble equivalence for perturbed ErdH{o}s-R'enyi random graphs." @default.
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