Asymptotic behavior of the generalized Derrida-Retaux recursive model

Zenghu Li; Run Zhang

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arXiv · 2411.13068

Asymptotic behavior of the generalized Derrida-Retaux recursive model

Zenghu Li·Run Zhang

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Abstract

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 a 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.

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Zenghu Li, Run Zhang. 2024-11-20. Asymptotic behavior of the generalized Derrida-Retaux recursive model. https://arxiv.org/abs/2411.13068

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