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<p>We study the max-type recursive model introduced by Hu and Shi (J. Stat. Phys., 2018), which generalizes the model of Derrida and Retaux (J. Stat. Phys., 2014). The class of geometric-type marginal distributions is preserved by the model with geometric offspring distribution. We give some long-time asymptotic expansions of the parameters of the marginal distribution. From the expansions, we derive the asymptotics of the sustainability probability, marginal distribution, first moment and probability generating function.</p>

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Asymptotic Behavior of the Generalized Derrida–Retaux Recursive Model

  • 期刊论文

  • 发表日期：

    2025年7月16日

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  • Zenghu Li,
  • Run Zhang

摘要

We study the max-type recursive model introduced by Hu and Shi (J. Stat. Phys., 2018), which generalizes the model of Derrida and Retaux (J. Stat. Phys., 2014). The class of geometric-type marginal distributions is preserved by the model with geometric offspring distribution. We give some long-time asymptotic expansions of the parameters of the marginal distribution. From the expansions, we derive the asymptotics of the sustainability probability, marginal distribution, first moment and probability generating function.