Balázs Ráth: Frozen percolation on the binary tree is nonendogenous

Speaker. Balázs Ráth

Title: Frozen percolation on the binary tree is nonendogenous

Abstract: In frozen percolation, i.i.d. uniformly distributed clocks are assigned to the edges of a graph. When its clock rings, an edge opens provided neither of its endvertices is part of an infinite open cluster; in the opposite case, it freezes. Aldous (2000) showed that frozen percolation is well-defined on the infinite 3-regular tree. However, it was not known whether the set of frozen edges is a measurable function w.r.t. the sigma-algebra generated by the clocks. We give a negative answer to this question, or, using terminology introduced by Aldous and Bandyopadhyay (2005), we show that frozen percolation on the binary tree is nonendogenous. An essential role in our proofs is played by a modified frozen percolation process that has nice scale invariant properties. Joint work with Jan Swart and Tamas Terpai.