# The Derrida--Retaux conjecture on recursive models

Abstract : We are interested in the nearly supercritical regime in a family of max-type recursive models studied by Derrida and Retaux, and prove that under a suitable integrability assumption on the initial distribution, the free energy vanishes at the transition with an essential singularity with exponent $\tfrac12$. This gives a weaker answer to a conjecture of Derrida and Retaux. Other behaviours are obtained when the integrability condition is not satisfied.
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https://hal.archives-ouvertes.fr/hal-02222897
Contributor : Inspire Hep <>
Submitted on : Thursday, August 1, 2019 - 2:05:06 AM
Last modification on : Wednesday, August 14, 2019 - 7:37:50 AM

### Citation

Xinxing Chen, Victor Dagard, Bernard Derrida, Yueyun Hu, Mikhail Lifshits, et al.. The Derrida--Retaux conjecture on recursive models. 2019. ⟨hal-02222897⟩

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