Abstract:In this paper we establish a strong decoupling inequality for the cylinder's percolation process introduced by Tykesson and Windisch in [18]. This model features a very strong dependency structure, making it difficult to study, and this is why such decoupling inequalities are desirable. It is important to notice that the type of dependencies featured by cylinder's percolation is particularly intricate, given that the cylinders have infinite range (unlike some models like Boolean percolation) while at the same … Show more
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