We investigate the rank of the adjacency matrix of large diluted random graphs: for a sequence of graphs (G n ) n≥0 converging locally to a Galton—Watson tree T (GWT), we provide an explicit formula ...

The Annals of Applied Probability, Vol. 16, No. 1 (Feb., 2006), pp. 295-309 (15 pages) We consider the discrete Laplace operator $\Delta ^{(N)}$ on Erdős-Rényi random graphs with N vertices and edge ...

Graph limit theory provides a rigorous framework for analysing sequences of large graphs by representing them as continuous objects known as graphons – symmetric measurable functions on the unit ...

When the mathematicians Jeff Kahn and Gil Kalai first posed their “expectation threshold” conjecture in 2006, they didn’t believe it themselves. Their claim — a broad assertion about mathematical ...

Venture capital firms use a variety of accumulated resources to inform their investment activities, but do the rely solely on their own resources or do they employ other firms' resources to complement ...