Recently, the asymptotic mean value of the height for a birth-and-death process is given in Videla [Videla, L.A. (2020)]. We consider the asymptotic variance of the height in the case when the number of states tends to infinity. Further, we prove that the heights exhibit a cutoff phenomenon and that the normalized height converges to a degenerate distribution.

中文翻译：

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关于生死过程的高度渐近行为的注释

最近，Videla [Videla, LA (2020)] 给出了生死过程的高度渐近平均值。我们考虑在状态数趋于无穷大的情况下高度的渐近方差。此外，我们证明了高度表现出截止现象，并且归一化高度收敛到退化分布。