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arXiv · 1403.3516

A sharp threshold for collapse of the random triangular group

Sylwia Antoniuk·Ehud Friedgut·Tomasz Łuczak
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Abstract

The random triangular group $\Gamma(n,p)$ is the group given by a random group presentation with $n$ generators in which every relator of length three is present independently with probability $p$. We show that in the evolution of $\Gamma(n,p)$ the property of collapsing to the trivial group admits a very sharp threshold.

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Sylwia Antoniuk, Ehud Friedgut, Tomasz Łuczak. 2014-03-14. A sharp threshold for collapse of the random triangular group. https://arxiv.org/abs/1403.3516

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