A matrix model for random nilpotent groups

2016/02/03 by Kelly Delp, Delp, Kelly, Tullia Dymarz +3
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #Probability (math.PR) #math.GR #math.PR

paper · pdf · doi:10.48550/arxiv.1602.01454

21 pages

arxiv created 2016/02/03 · arxiv updated 2016/02/04

Abstract

We study random torsion-free nilpotent groups generated by a pair of random words of length ℓ in the standard generating set of U_n(ℤ). Specifically, we give asymptotic results about the step properties of the group when the lengths of the generating words are functions of n. We show that the threshold function for asymptotic abelianness is ℓ = c √(n), for which the probability approaches e^-2c2, and also that the threshold function for having full-step, the same step as U_n(ℤ), is between c n² and c n³.

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