Rank one HCIZ at high temperature: interpolating between classical and free convolutions
We study the rank one Harish-Chandra-Itzykson-Zuber integral in the limit where \frac{N\beta}{2} \to cNβ2→c, called the high-temperature regime and show that it can be used to construct a promising one-parameter interpolation family, with parameter c between the classical and the free convolution. This c-convolution has a simple interpretation in terms of another associated family of distribution indexed by c, called the Markov-Krein transform: the c-convolution of two distributions corresponds to the classical convolution of their Markov-Krein transforms. We derive first cumulant-moment relations, a central limit theorem, a Poisson limit theorem and show several numerical examples of c-convoluted distributions.
1996 ◽
Vol 33
(01)
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pp. 146-155
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1983 ◽
Vol 20
(01)
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pp. 47-60
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2002 ◽
Vol 43
(12)
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pp. 6224-6237
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1990 ◽
Vol 1
(2)
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pp. 231-242
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2004 ◽
Vol 48
(1)
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pp. 1-20
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