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2018 A spectral decomposition for the block counting process and the fixation line of the beta(3,1)-coalescent
Martin Möhle
Electron. Commun. Probab. 23: 1-15 (2018). DOI: 10.1214/18-ECP203

Abstract

A spectral decomposition for the generator of the block counting process of the $\beta (3,1)$-coalescent is provided. This decomposition is strongly related to Riordan matrices and particular Fuss–Catalan numbers. The result is applied to obtain formulas for the distribution function and the moments of the absorption time of the $\beta (3,1)$-coalescent restricted to a sample of size $n$. We also provide the analog spectral decomposition for the fixation line of the $\beta (3,1)$-coalescent. The main tools in the proofs are generating functions and Siegmund duality. Generalizations to the $\beta (a,1)$-coalescent with parameter $a\in (0,\infty )$ are discussed leading to fractional differential or integral equations.

Citation

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Martin Möhle. "A spectral decomposition for the block counting process and the fixation line of the beta(3,1)-coalescent." Electron. Commun. Probab. 23 1 - 15, 2018. https://doi.org/10.1214/18-ECP203

Information

Received: 11 July 2018; Accepted: 17 December 2018; Published: 2018
First available in Project Euclid: 22 December 2018

zbMATH: 07023491
MathSciNet: MR3896840
Digital Object Identifier: 10.1214/18-ECP203

Subjects:
Primary: 60J10, 60J27
Secondary: 05C05, 92D15

JOURNAL ARTICLE
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