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The pillowcase distribution and near-involutions
In the context of the Eskin-Okounkov approach to the calculation of the
volumes of the different strata of the moduli space of quadratic differentials,
the important ingredients are the pillowcase weight probability distribution on
the space of Young diagrams, and the asymptotic study of characters of
permutations that near-involutions. In this paper we present various new
results for these objects. Our results give light to unforeseen difficulties in
the general solution to the problem, and they simplify some of the previous
proofs.Comment: This paper elaborates on some of the results of the author's PhD
thesis (arXiv:1209.4333). This is the published version,
http://ejp.ejpecp.org/article/view/362
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