Abstract
I consider a simple birth-death model with an absorbing state, where the stable fixed point of the corresponding deterministic mean-field dynamics turns into a transient peak of the probability distribution due to the presence of a tiny fluctuation. The model satisfies the detailed-balance condition, enabling one not only to obtain the analytic form of a quasi-stationary distribution, but also to obtain the analytic form of the escape time under the assumption of quasi-stationarity. I argue that the quasi-steady distribution with exponentially decaying normalization is an excellent approximation of the dynamics at late times, especially for small fluctuations. The analytic expressions for the quasi-stationary distribution and the escape time are expected to be more accurate, hence more useful, for systems with larger sizes.
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Acknowledgments
This work was supported by the National Research Foundation of Korea, funded by the Ministry of Education (NRF-2020R1A2C1005956).
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Lee, J. Analytic Form of the Quasi-stationary Distribution of a Simple Birth-Death Process. J. Korean Phys. Soc. 77, 457–462 (2020). https://doi.org/10.3938/jkps.77.457
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DOI: https://doi.org/10.3938/jkps.77.457