For a geometric-offspring generalized Derrida-Retaux model, the marginal parameters have explicit asymptotic expansions in every regime, yielding sharp decay rates for the survival probability and mean.
The Derrida-Retaux model on a geometric Galton-Watson tree
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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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Asymptotic behavior of the generalized Derrida-Retaux recursive model
For a geometric-offspring generalized Derrida-Retaux model, the marginal parameters have explicit asymptotic expansions in every regime, yielding sharp decay rates for the survival probability and mean.