Colloquium Mathematics - Prof. M. Heydenreich

Abstract:
Percolation is a paradigmatic model in modern Probability Theory,
where one starts from a (mostly infinite) graph G, and then samples a
random subgraph with prescribed intensity. Despite its fairly easy
mechanism, percolation exhibits a phase transition, and understanding
properties at the phase transition point (so-called critical behavior)
is of highest interest.

In my talk I review a number of results particularly for the case when
G is the high-dimensional lattice. Of particular interest are the
special properties of random walk on critical percolation clusters. In
the second part, I am focusing on current work about a continuum
percolation model known as the random connection model.