Sharp Threshold Phenomena in Percolation

Sharp Threshold Phenomena in Percolation

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Hugo Duminil-Copin, IHES
TBD

In this second talk, we will present the theory of sharp thresholds which can be understood as a mathematical equivalent of phase transitions in physics. In particular, we will illustrate how abstract theorems on Boolean functions can help understanding the phase transition of a model of random subgraphs of a given lattice, called percolation, which plays an essential role in probability. Among other results, we will explain how the Bourgain-Kahn-Katznelson-Kalai-Linial theorem and the O’Donnell-Saks-Schramm-Servedio inequality can be used to compute critical points and to prove exponential decay of correlations away from these critical points.