Approximating the Cumulant Generating Function of Triangles in the Erdos–Renyi Random Graph
Cristian Giardinà, Claudio Giberti · IRIS UNIMORE (University of Modena and Reggio Emilia) · 2021
We study the pressure of the "edge-triangle model", which is equivalent to the cumulant generating function of triangles in the Erdös-Rényi 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.