We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
A train track directed random walk on (F<sub>r</sub>).
- Authors
Kapovich, Ilya; Pfaff, Catherine
- Abstract
Several known results, by Rivin, Calegari-Maher and Sisto, show that an element φn ∈ (Fr), obtained after n steps of a simple random walk on (Fr), is fully irreducible with probability tending to 1 as n → ∞. In this paper, we construct a natural "train track directed" random walk 풲 on (Fr) (where r ≥ 3). We show that, for the element φn ∈ (Fr), obtained after n steps of this random walk, with asymptotically positive probability the element φn has the following properties: φn is an ageometric fully irreducible, which admits a train track representative with no periodic Nielsen paths and exactly one nondegenerate illegal turn, that φn has "rotationless index" (so that the geometric index of the attracting tree Tφn of φn is 2r - 3), has index list and the ideal Whitehead graph being the complete graph on 2r - 1 vertices, and that the axis bundle of φn in the Outer space r consists of a single axis.
- Subjects
RANDOM walks; PROBABILITY theory; NON-degenerate perturbation theory; GRAPH theory; AUTOMORPHISMS; MATHEMATICAL analysis
- Publication
International Journal of Algebra & Computation, 2015, Vol 25, Issue 5, p745
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196715500186