Frédérique Bassino ; Cyril Nicaud ; Pascal Weil

Generic properties of random subgroups of a free group for general distributions
dmtcs:2991 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2012,
DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12)

https://doi.org/10.46298/dmtcs.2991
Generic properties of random subgroups of a free group for general distributions
Authors: Frédérique Bassino ; Cyril Nicaud ; Pascal Weil
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Frédérique Bassino;Cyril Nicaud;Pascal Weil
We consider a generalization of the uniform wordbased distribution for finitely generated subgroups of a free group. In our setting, the number of generators is not fixed, the length of each generator is determined by a random variable with some simple constraints and the distribution of words of a fixed length is specified by a Markov process. We show by probabilistic arguments that under rather relaxed assumptions, the good properties of the uniform wordbased distribution are preserved: generically (but maybe not exponentially generically), the tuple we pick is a basis of the subgroup it generates, this subgroup is malnormal and the group presentation defined by this tuple satisfies a small cancellation condition.
Volume: DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12)
Section: Proceedings
Published on: January 1, 2012
Imported on: January 31, 2017
Keywords: [MATH.MATHCO] Mathematics [math]/Combinatorics [math.CO],[MATH.MATHGR] Mathematics [math]/Group Theory [math.GR],[INFO.INFODS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]