We prove that a uniform rooted plane map with n edges converges in distribution after a suitable normalization to the Brownian map for the Gromovâ€“Hausdorff topology. A recent bijection due to AmbjÃ¸rnâ€¦ (More)

We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favouring short distances and high degrees. Theâ€¦ (More)

The integrated Brownian motion is sometimes known as the Langevin process. Lachal studied several excursion laws induced by the latter. Here we follow a different point of view developed by Pitmanâ€¦ (More)

Opal has long fascinated scientists. It is one of the few minerals with an amorphous structure, and yet, compared to silica glass, it is highly organized on the mesoscale. By means of inelasticâ€¦ (More)

We study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is aâ€¦ (More)

A growing family of random graphs is called robust if it retains a giant component after percolation with arbitrary positive retention probability. We study robustness for graphs, in which newâ€¦ (More)