Journal of Applied Probability

Asymptotic hitting probabilities for the Bolthausen-Sznitman coalescent

Martin Möhle


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

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

First available in Project Euclid: 2 December 2014

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Zentralblatt MATH identifier

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

Asymptotic hitting probability Bolthausen-Sznitman coalescent generating function


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

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