Bootstrap percolation in random geometric graphs
Random geometric graphs were invented by E.N. Gilbert in 1961 to model communications networks. Bootstrap percolation was invented by Chalupa, Leath and Reich in 1979 to model magnetism. Both models have since been used to study many other things. This is because many spatial networks, such as the brain, can be modeled as random geometric graphs, and many natural processes on networks, such as the activation of neurons in the brain, or the spread of beliefs on social media, can be modeled by bootstrap percolation. So it was natural when, in 2014, Bradonjic and Saniee put the two models together, and studied bootstrap percolation in random geometric graphs. In my talk, I’ll describe an (almost) complete solution of the Bradonjic-Saniee model, obtained jointly with Victor Falgas-Ravry. The proofs use variational methods, tiling arguments, and discrete isoperimetric inequalities.