Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
studying typical properties of finitely presented groups
|
| gptkbp:defines |
A model for constructing random finitely presented groups by randomly choosing relators.
|
| gptkbp:densityModel |
Gromov density model
|
| gptkbp:field |
geometric group theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Gromov's random groups
|
| gptkbp:introduced |
gptkb:Mikhail_Gromov
|
| gptkbp:introducedIn |
1993
|
| gptkbp:notableAchievement |
Phase transition at density 1/2
For density > 1/2, random groups are trivial or isomorphic to Z/2Z with overwhelming probability. For density < 1/2, random groups are infinite and hyperbolic with overwhelming probability. |
| gptkbp:property |
At certain densities, random groups are infinite, hyperbolic, and torsion-free with high probability.
|
| gptkbp:publishedIn |
M. Gromov, 'Asymptotic invariants of infinite groups', 1993
|
| gptkbp:relatedTo |
gptkb:Weyl_group
group presentation hyperbolic group probabilistic method in group theory random group |
| gptkbp:studiedBy |
gptkb:Igor_Rivin
Martin Lustig Yann Ollivier |
| gptkbp:bfsParent |
gptkb:Misha_Gromov
|
| gptkbp:bfsLayer |
7
|