Almost all one-relator groups with at least three generators are residually finite
arXiv:0809.4693
Abstract
We prove that with probability tending to 1, a 1-relator group with at least 3 generators and relator of length n is residually finite, virtually residually (finite p)-group for all sufficiently large p, and coherent. The proof uses both combinatorial group theory and non-trivial results about Brownian motions, bridges and excursions in R^k.
11 pages. Comments are welcome. v2: Added a new probabilistic model: counting 1-relataed groups up o isomorphism, not words as before