Oriented Random Walk on the Heisenberg Group and Percolation

2022/02/03 by Benjamini, Itai, Schramm, Oded
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2202.01519

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, the infinite cluster of percolation with retention parameter p, close enough to 1, is transient.

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