2014/07/14 by Horbez, Camille
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Probability (math.PR)
paper · doi:10.48550/arxiv.1407.3608
We show that the horoboundary of outer space for the Lipschitz metric is a quotient of Culler and Morgan's classical boundary, two trees being identified whenever their translation length functions are homothetic in restriction to the set of primitive elements of FN. We identify the set of Busemann points with the set of trees with dense orbits. We also investigate a few properties of the horoboundary of outer space for the backward Lipschitz metric, and show in particular that it is infinite-dimensional when N≥ 3. We then use our description of the horoboundary of outer space to derive an analogue of a theorem of Furstenberg--Kifer and Hennion for random products of outer automorphisms of FN, that estimates possible growth rates of conjugacy classes of elements of FN under such products.