The probability measure corresponding to 2-plane trees (Q2874345)
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scientific article; zbMATH DE number 6251967
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The probability measure corresponding to 2-plane trees |
scientific article; zbMATH DE number 6251967 |
Statements
29 January 2014
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beta distribution
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Mellin convolution
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additive and multiplicative free convolution
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Marchenko-Pastur distribution
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moment sequence
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math.PR
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math.CO
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The probability measure corresponding to 2-plane trees (English)
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The authors investigate the properties of the probability measure representing the moment sequence \(\{{3n\choose n}\frac{1}{n+1}\}\). The first shows that this measure is the Mellin convolution of two beta distributions, and so it is absolutely continuous. Then they find its density function of this measure and prove that it is infinitely divisible with respect to additive free convolutions.
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