Invariant random graphs with iid degrees in a general geography
Let \(G\) be an infinite transitive finite-degree graph specifying the space geography into which an automorphism-invariant random graph with specified degree distribution should be defined. The existence of such random graphs is investigated when \(G\) has polynomial, exponential, or intermediate growth rate. Conditions are given on the expected edge lengths and on the degree distribution. Special cases of \(G\) considered are integer lattices and regular trees of degree three or more. More exotic geographies include the Trofimov graph, the Diestel-Leader graphs, and the Grigorchuk group.
scientific article; zbMATH DE number 5553446