Analysis of generating functions and probabilities on trees (Q2769672)
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scientific article; zbMATH DE number 1701853
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Analysis of generating functions and probabilities on trees |
scientific article; zbMATH DE number 1701853 |
Statements
5 February 2002
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families of tree
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asymptotic estimates
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number of rooted trees
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contour process
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Brownian excursion
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Analysis of generating functions and probabilities on trees (English)
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The author considers simply generated families of tree and employs analytic tools, the saddle point method and singularity analysis, in order to obtain asymptotic estimates for the coefficients of generating functions counting trees with specific parameters. As an application, he proves an asymptotic formula for the number of rooted trees in a simply generated family of size \(n\) with \(l\) leaves such that the \(m\)th leaf has height \(k\). Under suitable conditions the height of the \(m\)th leaf is Maxwell distributed. He also states that the corresponding contour process converges to Brownian excursion.NEWLINENEWLINEFor the entire collection see [Zbl 0968.00043].
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