English

Oriented Random Walk on the Heisenberg Group and Percolation

Probability 2022-02-04 v1

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 Z,Z2\mathbb{Z}, \mathbb{Z}^2, the infinite cluster of percolation with retention parameter pp, close enough to 11, is transient.

Keywords

Cite

@article{arxiv.2202.01519,
  title  = {Oriented Random Walk on the Heisenberg Group and Percolation},
  author = {Itai Benjamini and Oded Schramm},
  journal= {arXiv preprint arXiv:2202.01519},
  year   = {2022}
}

Comments

Written in 1998, 6 pages. arXiv admin note: text overlap with arXiv:math/9701227

R2 v1 2026-06-24T09:17:33.580Z