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), m ∈ N, 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.
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