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.

Approximating the Cumulant Generating Function of Triangles in the Erdös–Rényi Random Graph / Giardina', Cristian; Giberti, Claudio; Magnanini, Elena. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 182:2(2021), pp. 1-22. [10.1007/s10955-021-02707-3]

Approximating the Cumulant Generating Function of Triangles in the Erdös–Rényi Random Graph

Cristian Giardinà;Claudio Giberti
;
2021

Abstract

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.
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Approximating the Cumulant Generating Function of Triangles in the Erdös–Rényi Random Graph / Giardina', Cristian; Giberti, Claudio; Magnanini, Elena. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 182:2(2021), pp. 1-22. [10.1007/s10955-021-02707-3]
Giardina', Cristian; Giberti, Claudio; Magnanini, Elena
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1230577
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