Journal of Applied Probability

Asymptotic hitting probabilities for the Bolthausen-Sznitman coalescent

Martin Möhle

Abstract

The probability h(n, m) that the block counting process of the Bolthausen-Sznitman n-coalescent ever visits the state m is analyzed. It is shown that the asymptotic hitting probabilities h(m) = limn→∞h(n, m), mN, exist and an integral formula for h(m) is provided. The proof is based on generating functions and exploits a certain convolution property of the Bolthausen-Sznitman coalescent. It follows that h(m) ∼ 1/log m as m → ∞. An application to linear recursions is indicated.

Article information

Source
J. Appl. Probab., Volume 51A (2014), 87-97.

Dates
First available in Project Euclid: 2 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1417528469

Digital Object Identifier
doi:10.1239/jap/1417528469

Mathematical Reviews number (MathSciNet)
MR3317352

Zentralblatt MATH identifier
1297.68030

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60C05: Combinatorial probability
Secondary: 05C05: Trees 92D15: Problems related to evolution

Keywords
Asymptotic hitting probability Bolthausen-Sznitman coalescent generating function

Citation

Möhle, Martin. Asymptotic hitting probabilities for the Bolthausen-Sznitman coalescent. J. Appl. Probab. 51A (2014), 87--97. doi:10.1239/jap/1417528469. https://projecteuclid.org/euclid.jap/1417528469


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