Near-critical and frozen percolation

Motivated by sol-gel transitions, David Aldous (2000) introduced and analysed a fascinating dynamic percolation model on a tree where clusters stop growing (freeze') as soon as they become infinite.

In this talk I will discuss recent and ongoing work (with Demeter Kiss and Pierre Nolin) on processes of similar flavour on planar lattices. We focus on the question whether the giant (i.e. frozen') clusters occupy a negligible, moderate or very large fraction of space. A related question is whether microscopic `trapped' regions occur. It turns out that the behaviour is very different from that for trees. Accurate results for near-critical percolation play an important role in the analysis.