Almost all one-relator groups with at least three generators are residually finite

摘要

We prove that with probability tending to 1, a 1-relator group with at least3 generators and relator of length n is residually finite, virtually residually(finite p)-group for all sufficiently large p, and coherent. The proof usesboth combinatorial group theory and non-trivial results about Brownian motions,bridges and excursions in R^k.