Our papers are the official record of our discoveries. They allow others to build on and apply our work. Each paper is the result of many months of research, so we make a special effort to make them clear, beautiful and inspirational, and publish them in leading journals.
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Percolation theory
FC
MB
FC Journal of Statistical MechanicsClusters of neurons
Percolation theory shows that the formation of giant clusters of neurons relies on a few parameters that could be measured experimentally.
Percolation theory
PBBB
MP
PS
Transactions of the American Mathematical SocietyBootstrap percolation models
A subset of bootstrap percolation models, which stabilise systems of cells on infinite lattices, exhibit non-trivial phase transitions.
Percolation theory
FBMP
SIAM Journal on Discrete MathematicsMaximum percolation time
A simple formula gives the maximum time for an n x n grid to become entirely infected having undergone a bootstrap percolation process.
Percolation theory
BB
KGCJMP Electronic Journal of ProbabilityPercolation on Galton-Watson trees
The critical probability for bootstrap percolation, a process which mimics the spread of an infection in a graph, is bounded for Galton-Watson trees.