Spatial Networks and Percolation

Abstract

The classical percolation problem is to find whether there is an infinite connected component in a random set created by removing edges from a $d$-dimensional lattice, independently at random. Since its introduction into the mathematical literature by Broadbent and Hammersley (1957) the subject of percolation has developed in many ways and is now one of the most exciting and active research areas in probability and statistical mechanics. In this workshop, we focused on current trends, including percolation on point sets with correlations, on spatial random graphs and networks with scale-free degree distribution or long-range edge distribution, percolation of random sets like level set of Gaussian fields or the vacant set of interlacements, conformally invariant percolation structures in the plane, and random walks or information diffusion on percolation clusters. The workshop brought together more than sixty experts and promising young researchers from probability, statistical mechanics and computer science working on all aspects of percolation and spatial networks for an unprecedented exchange of new ideas and methods, with outstanding high quality online talks.