A Harris-Kesten theorem for confetti percolation

Christian Hirsch

Published 2012-04-26, updated 2013-12-27Version 5

Percolation properties of the dead leaves model, also known as confetti percolation, are considered. More precisely, we prove that the critical probability for confetti percolation with square-shaped leaves is 1/2. This result is related to a question of Benjamini and Schramm concerning disk-shaped leaves and can be seen as a variant of the Harris-Kesten theorem for bond percolation. The proof is based on techniques developed by Bollob\'as and Riordan to determine the critical probability for Voronoi and Johnson-Mehl percolation.