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Article Dans Une Revue Annals of Probability Année : 2021

The Derrida–Retaux conjecture on recursive models

Résumé

We are interested in the nearly supercritical regime in a family of max-type recursive models studied by Collet, Eckman, Glaser and Martin (Comm. Math. Phys. 94 (1984) 353–370) and by Derrida and Retaux (J. Stat. Phys. 156 (2014) 268–290) 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 12. This gives a weaker answer to a conjecture of Derrida and Retaux (J. Stat. Phys. 156 (2014) 268–290). Other behaviours are obtained when the integrability condition is not satisfied.

Dates et versions

hal-02222897 , version 1 (01-08-2019)

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Xinxing Chen, Victor Dagard, Bernard Derrida, Yueyun Hu, Mikhail Lifshits, et al.. The Derrida–Retaux conjecture on recursive models. Annals of Probability, 2021, 49 (2), pp.637-670. ⟨10.1214/20-AOP1457⟩. ⟨hal-02222897⟩
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