{"docId":2991,"paperId":2991,"url":"https:\/\/dmtcs.episciences.org\/2991","doi":"10.46298\/dmtcs.2991","journalName":"Discrete Mathematics & Theoretical Computer Science","issn":"","eissn":"1365-8050","volume":[{"vid":262,"name":"DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12)"}],"section":[{"sid":66,"title":"Proceedings","description":[]}],"repositoryName":"Hal","repositoryIdentifier":"hal-00687981","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-00687981v1","dateSubmitted":"2017-01-31 10:21:48","dateAccepted":null,"datePublished":"2012-01-01 00:00:00","titles":{"en":"Generic properties of random subgroups of a free group for general distributions"},"authors":["Bassino, Fr\u00e9d\u00e9rique","Nicaud, Cyril","Weil, Pascal"],"abstracts":{"en":"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."},"keywords":["[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]"]}