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Random Artin groups
Antoine Goldsborough and Nicolas Vaskou |
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Algebraic & Geometric Topology 25 (2025) 1523–1544
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Abstract |
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We introduce a new model of random Artin groups. The two variables we consider are the rank of the Artin groups and the set of permitted coefficients of their defining graphs. The heart of our model is to control the speed at which we make that set of permitted coefficients grow relatively to the growth of the rank of the groups, as it turns out different speeds yield very different results. We describe these speeds by means of (often polynomial) functions. In this model, we show that for a large range of such functions, a random Artin group satisfies most conjectures about Artin groups asymptotically almost surely. Our work also serves as a study of how restrictive the commonly studied families of Artin groups are, as we compute explicitly the probability that a random Artin group belongs to various families of Artin groups, such as the classes of -dimensional Artin groups, FC-type Artin groups, large-type Artin groups, and others. |
Keywords
geometric group theory, Artin groups, random groups
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Mathematical Subject Classification
Primary: 20F36, 20F65, 20F69, 20P05
Secondary: 20F67
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References |
Publication
Received: 25 January 2023
Revised: 30 October 2023
Accepted: 17 November 2023
Published: 20 June 2025
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Authors |
| Antoine Goldsborough | |
| School of Mathematics & Computer
Sciences Heriot-Watt University Edinburgh United Kingdom |
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| Nicolas Vaskou | |
| Department of Mathematics University of Bristol Bristol United Kingdom |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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