10.46298/dmtcs.2991
https://dmtcs.episciences.org/2991
Bassino, Frédérique
Frédérique
Bassino
0000-0002-0127-9352
Nicaud, Cyril
Cyril
Nicaud
Weil, Pascal
Pascal
Weil
Generic properties of random subgroups of a free group for general distributions
We consider a generalization of the uniform word-based 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 word-based 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.
episciences.org
[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]
[MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]
[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]
2023-03-22
2012-01-01
2012-01-01
en
journal article
https://hal.science/hal-00687981v1
1365-8050
https://dmtcs.episciences.org/2991/pdf
VoR
application/pdf
Discrete Mathematics & Theoretical Computer Science
DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12)
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