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arXiv · 2502.02991

The Derrida-Retaux model on a geometric Galton-Watson tree

Gerold Alsmeyer·Yueyun Hu·Bastien Mallein
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Abstract

We consider a generalized Derrida-Retaux model on a Galton-Watson tree with a geometric offspring distribution. For a class of recursive systems, including the Derrida-Retaux model with either a geometric or exponential initial distribution, we characterize the critical curve using an involution-type equation and prove that the free energy satisfies the Derrida-Retaux conjecture.

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Gerold Alsmeyer, Yueyun Hu, Bastien Mallein. 2025-02-05. The Derrida-Retaux model on a geometric Galton-Watson tree. https://arxiv.org/abs/2502.02991

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