A spectral decomposition for the block counting process and the fixation line of the beta(3,1)-coalescent

DOI10.1214/18-ECP203zbMath1406.60104OpenAlexW2905934730MaRDI QIDQ1725494

Martin Möhle

Publication date: 14 February 2019

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ecp/1545447666

zbMATH Keywords

generating functionspectral decompositionRiordan matrixfractional differential equationFuss-Catalan numbersabsorption timebeta coalescentsiegmund duality

Mathematics Subject Classification ID

Trees (05C05) Problems related to evolution (92D15) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Continuous-time Markov processes on discrete state spaces (60J27)

Cites Work

• A spectral decomposition for the block counting process of the Bolthausen-Sznitman coalescent
• Fuss-Catalan numbers in noncommutative probability
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• The coalescent
• The Riordan group
• The equivalence of absorbing and reflecting barrier problems for stochastically monotone Markov processes
• A unified approach to generalized Stirling numbers
• On Ruelle's probability cascades and an abstract cavity method
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Riordan arrays and combinatorial sums
• Coalescents with multiple collisions
• Particle representations for measure-valued population models
• A countable representation of the Fleming-Viot measure-valued diffusion
• On the block counting process and the fixation line of exchangeable coalescents
• The general coalescent with asynchronous mergers of ancestral lines
• On Asymptotics of the Beta Coalescents
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