Random length-spectrum rigidity for free groups

Author:
Ilya Kapovich

Journal:
Proc. Amer. Math. Soc. **140** (2012), 1549-1560

MSC (2010):
Primary 20Fxx; Secondary 57Mxx, 37Bxx, 37Dxx

DOI:
https://doi.org/10.1090/S0002-9939-2011-11030-X

Published electronically:
September 9, 2011

MathSciNet review:
2869139

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Abstract | References | Similar Articles | Additional Information

Abstract: We say that a subset is *spectrally rigid* if whenever are points of the (unprojectivized) outer space such that for every , then in . It is well known that 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 . We prove that if is a free basis of (where ), then almost every trajectory of a non-backtracking simple random walk on with respect to is a spectrally rigid subset of .

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Additional Information

**Ilya Kapovich**

Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801

Email:
kapovich@math.uiuc.edu

DOI:
https://doi.org/10.1090/S0002-9939-2011-11030-X

Received by editor(s):
May 21, 2010

Received by editor(s) in revised form:
January 24, 2011

Published electronically:
September 9, 2011

Additional Notes:
The author was supported by NSF grant DMS-0904200

Communicated by:
Alexander N. Dranishnikov

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.