Random Feynman Graphs

TL;DR

This paper explores a new class of random graph ensembles derived from Feynman graphs of multidimensional integrals, revealing their similarities to known models like CDRG and expanding understanding of graph structures in statistical mechanics.

Contribution

It introduces a novel class of random graph ensembles based on Feynman graphs of multidimensional integrals, generalizing previous relations to random graphs with hidden colors.

Findings

Ensembles resemble those in hidden color random graphs (CDRG)

Generalizes the relation between Feynman graphs and degree-distributed graphs

Provides a new perspective on graph structures in statistical mechanics

Abstract

We investigate a class of random graph ensembles based on the Feynman graphs of multidimensional integrals, representing statistical-mechanical partition functions. We show that the resulting ensembles of random graphs strongly resemble those defined in random graphs with hidden color (CDRG), generalizing the known relation of the Feynman graphs of simple one-dimensional integrals to random graphs with a given degree distribution.