2010/01/12 by Ilya Kapovich, Kapovich, Ilya
Mathematics · #20F #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:20F
paper · pdf · doi:10.48550/arxiv.1001.1729
12 pages, no figures; to appear in Proceedings of the American Mathematical Society; updated ref to the Duchin-Leininger-Rafi paper
arxiv created 2011/02/04 · arxiv updated 2011/02/07
We say that a subset S⊆ FN is spectrally rigid if whenever T1, T2∈ cvN are points of the (unprojectivized) Outer space such that ||g||T1=||g||T2 for every g∈ S then T1=T2 in \cvn. It is well-known that FN itself is spectrally rigid; it also follows from the result of Smillie and Vogtmann that there does not exist a finite spectrally rigid subset of FN. We prove that if A is a free basis of FN (where N≥ 2) then almost every trajectory of a non-backtracking simple random walk on FN with respect to A is a spectrally rigid subset of FN.