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 , the infinite cluster of percolation with retention parameter , close enough to , is transient.
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