By Ioana Dumitriu | published 2011-08-15 |
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We compute the exact and limiting smallest eigenvalue distributions for two
classes of $\beta$-Jacobi ensembles not covered by previous studies. In the
general $\beta$ case, these distributions are given by multivariate
hypergeometric ${}_2F_{1}^{2/\beta}$ functions, whose behavior can be analyzed
asymptotically for special values of $\beta$ which include $\beta \in
2\mathbb{N}_{+}$ as well as for $\beta = 1$. Interest in these objects stems
from their connections (in the $\beta = 1,2$ cases) to principal submatrices of
Haar-distributed (orthogonal, unitary) matrices appearing in randomized,
communication-optimal, fast, and stable algorithms for eigenvalue computations
\cite{DDH07}, \cite{BDD10}.
... http://arxiv.org/abs/1009.4677
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