期刊
JOURNAL OF STATISTICAL PHYSICS
卷 182, 期 2, 页码 -出版社
SPRINGER
DOI: 10.1007/s10955-021-02707-3
关键词
Erdos-Renyi random graph; Edge-triangle model; Rare events simulations; Phase transition; Graphs limits; Ensemble equivalence
Through population dynamics method and discretization of graphon variational problem, a curve in the parameter space where one-step replica symmetry breaking transition occurs is located. Sampling a large graph in the broken symmetry phase is well described by a graphon with a structure very close to an equi-bipartite graph.
We study the pressure of the edge-triangle model, which is equivalent to the cumulant generating function of triangles in the Erdos-Renyi random graph. The investigation involves a population dynamics method on finite graphs of increasing volume, as well as a discretization of the graphon variational problem arising in the infinite volume limit. As a result, we locate a curve in the parameter space where a one-step replica symmetry breaking transition occurs. Sampling a large graph in the broken symmetry phase is well described by a graphon with a structure very close to the one of an equi-bipartite graph.
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