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A Harris-Kesten theorem for confetti percolation. (English) Zbl 1323.60130
Summary: 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 I. Benjamini and O. Schramm [Probab. Theory Relat. Fields 111, No. 4, 551–564 (1998; Zbl 0910.60076)] 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 B. Bollobás and O. Riordan [Probab. Theory Relat. Fields 136, No. 3, 417–468 (2006; Zbl 1100.60054); Probab. Theory Relat. Fields 140, No. 3–4, 319–343 (2008; Zbl 1135.60057)] to determine the critical probability for Voronoi and Johnson-Mehl percolation.

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory
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