Character theory of symmetric groups, subgroup growth of Fuchsian groups, and random walks |
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Authors: | Thomas W Müller Jan-Christoph Schlage-Puchta |
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Institution: | a School of Mathematical Sciences, Queen Mary & Westfield College, University of London, Mile End Road, E1 4NS London, United Kingdom b Mathematisches Institut, Albert-Ludwigs-Universität, Eckerstr. 1, 79104 Freiburg, Germany |
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Abstract: | We develop a number of statistical aspects of symmetric groups (mostly dealing with the distribution of cycles in various subsets of Sn), asymptotic properties of (ordinary) characters of symmetric groups, and estimates for the multiplicities of root number functions of these groups. As main applications, we present an estimate for the subgroup growth of an arbitrary Fuchsian group, a finiteness result for the number of Fuchsian presentations of such a group (resolving a long-standing problem of Roger Lyndon), as well as a proof of a well-known conjecture of Roichman concerning the mixing time of random walks on symmetric groups. |
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Keywords: | 20C30 20E07 20H10 20P05 60B15 |
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