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arXiv · 2103.08522

Asymptotic absorption-time distributions in extinction-prone Markov processes

David Hathcock·Steven H. Strogatz
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Abstract

We characterize absorption-time distributions for birth-death Markov chains with an absorbing boundary. For "extinction-prone" chains (which drift on average toward the absorbing state) the asymptotic distribution is Gaussian, Gumbel, or belongs to a family of skewed distributions. The latter two cases arise when the dynamics slow down dramatically near the boundary. Several models of evolution, epidemics, and chemical reactions fall into these classes; in each case we establish new results for the absorption-time distribution. Applications to African sleeping sickness are discussed.

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BibTeXRIS

David Hathcock, Steven H. Strogatz. 2021-03-15. Asymptotic absorption-time distributions in extinction-prone Markov processes. https://doi.org/10.1103/physrevlett.128.218301

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