Random subgroups of linear groups are free

By Richard Aoun. 2010

51 citations recorded by the source corpus.

We show that on an arbitrary finitely generated non virtually solvable linear group, any two independent random walks will eventually generate a free subgroup. In fact, this will hold for an exponential number of independent random walks.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c5460d12c1486cbed8be437cf761bccdbf1a4a9c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Peter Sarnak
2. Nicolas Templier

In Geometry and Topology

1. Peter Sarnak
2. Alex Kontorovich
3. Gergely Harcos
4. Kannan Soundararajan
5. A. Reznikov
6. Nicolas Templier
7. V. Blomer
8. P. Michel

In Mathematical Physics

1. Peter Sarnak
2. V. Blomer
3. Gergely Harcos
4. P. Michel
5. Nicolas Templier
6. Kannan Soundararajan
7. Djordje Milićević
8. Alex Kontorovich

Citations in the corpus

• Notes on Thin Matrix Groups (2012, methodology): “If the A j are chosen at the m-th step of a µ-random walk (m →∞) and support (µ) generates SLn(Z), then this was proved in [Aoun 2011].”