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arXiv · 2202.01519

Oriented Random Walk on the Heisenberg Group and Percolation

Itai Benjamini·Oded Schramm
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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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Itai Benjamini, Oded Schramm. 2022-02-03. Oriented Random Walk on the Heisenberg Group and Percolation. https://arxiv.org/abs/2202.01519

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