Right-convergence of sparse random graphs (Q466899)

This paper studies right-convergence of a sequence of sparse random graphs. A sequence of \(n\)-vertex graphs \(G_n\), \(n\geq1\), is said to be right-converging with respect to a target graph \(W\) if the logarithm of the sum of homomorphism (from \(G_n\) to \(W\)) weights, normalized by \(n\), has a limit. Based on interpolation techniques, the author proves that the sequence of sparse Erdős-Rényi graphs is right-converging provided the tensor product associated with the target graph \(W\) satisfies some convexity property. Both continuous and discrete graphs \(W\) are addressed in the paper.