Models and Methods for Random Networks

Percolation 1: Lattice Percolation, Subcritical and Supercritical Phases

After tree percolation in the first lecture, we move to percolation on the 2-dimensional lattice, the most basic and well-studied structure in percolation theory. We show that the two dimensional lattice exhibits a phase transition between a sub-critical phase where all clusters of connected vertices are almost surely finite, and a super-critical phase where one giant component of connected emerges.

Course Materials

Homework

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