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Oriented Random Walk on the Heisenberg Group and Percolation

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arxiv 2202.01519 v1 pith:CPEX4JNA submitted 2022-02-03 math.PR

classification math.PR
keywords groupheisenbergmathbborientedpercolationrandomwalkadmits
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abstract

It is shown that oriented random walk on the Heisenberg group admits exponential intersection tail. As a corollary we get that on any transitive graph of polynomial volume growth, which is not a finite extension of $\mathbb{Z}, \mathbb{Z}^2$, the infinite cluster of percolation with retention parameter $p$, close enough to $1$, is transient.

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