{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,25]],"date-time":"2024-03-25T16:40:32Z","timestamp":1711384832403},"reference-count":33,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2015,8]]},"abstract":"<jats:p> Several known results, by Rivin, Calegari-Maher and Sisto, show that an element \u03c6<jats:sub>n<\/jats:sub> \u2208 Out (F<jats:sub>r<\/jats:sub>), obtained after n steps of a simple random walk on Out (F<jats:sub>r<\/jats:sub>), is fully irreducible with probability tending to 1 as n \u2192 \u221e. In this paper, we construct a natural \"train track directed\" random walk \ud835\udcb2 on Out (F<jats:sub>r<\/jats:sub>) (where r \u2265 3). We show that, for the element \u03c6<jats:sub>n<\/jats:sub> \u2208 Out (F<jats:sub>r<\/jats:sub>), obtained after n steps of this random walk, with asymptotically positive probability the element \u03c6<jats:sub>n<\/jats:sub> has the following properties: \u03c6<jats:sub>n<\/jats:sub> is an ageometric fully irreducible, which admits a train track representative with no periodic Nielsen paths and exactly one nondegenerate illegal turn, that \u03c6<jats:sub>n<\/jats:sub> has \"rotationless index\" [Formula: see text] (so that the geometric index of the attracting tree T<jats:sub>\u03c6<jats:sub>n<\/jats:sub><\/jats:sub> of \u03c6<jats:sub>n<\/jats:sub> is 2r - 3), has index list [Formula: see text] and the ideal Whitehead graph being the complete graph on 2r - 1 vertices, and that the axis bundle of \u03c6<jats:sub>n<\/jats:sub> in the Outer space CV <jats:sub>r<\/jats:sub> consists of a single axis. <\/jats:p>","DOI":"10.1142\/s0218196715500186","type":"journal-article","created":{"date-parts":[[2015,5,8]],"date-time":"2015-05-08T03:39:12Z","timestamp":1431056352000},"page":"745-798","source":"Crossref","is-referenced-by-count":7,"title":["A train track directed random walk on <font>Out<\/font>(F<sub>r<\/sub>)"],"prefix":"10.1142","volume":"25","author":[{"given":"Ilya","family":"Kapovich","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801, USA"}]},{"given":"Catherine","family":"Pfaff","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, University of Bielefeld, Postfach 100131, Universit\u00e4tsstrasse 25, D-33501 Bielefeld, Germany"}]}],"member":"219","published-online":{"date-parts":[[2015,8,13]]},"reference":[{"key":"rf1","doi-asserted-by":"crossref","first-page":"85","DOI":"10.4310\/jdg\/1214447806","volume":"35","author":"Bestvina M.","year":"1992","journal-title":"J. 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