A Harris-Kesten theorem for confetti percolation

TL;DR

This paper establishes that the critical probability for confetti percolation with square leaves is 1/2, extending Harris-Kesten type results to this geometric percolation model.

Contribution

It proves the critical probability for square-shaped confetti percolation is 1/2, connecting it to Harris-Kesten theorem and related percolation models.

Findings

Critical probability for square confetti percolation is 1/2

Extension of Harris-Kesten theorem to confetti percolation

Methodology based on Bollobás and Riordan's techniques

Abstract

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.