On The Volume Of A Metric Ball In Unitary Group
2015 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT)(2015)
摘要
Volume estimates of metric balls in manifolds find diverse applications in communications and information theory. In this paper, we derive some new results for the volume of a metric ball in unitary group under Frobenius norm topological metric. Our first result is an integral representation of the exact volume, which involves a Toeplitz determinant of Bessel functions. The connection to matrix-variate hypergeometric functions leads from the exact finite size formula to an asymptotic one. The convergence of the obtained limiting formula is exceptionally fast due to the underlying mock-Gaussian behavior.
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关键词
metric ball,unitary group,communication theory,information theory,Frobenius norm topological metric,integral representation,Toeplitz determinant,Bessel functions,matrix-variate hypergeometric functions,mock-Gaussian behavior
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