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The Derrida--Retaux conjecture on recursive models

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arxiv 1907.01601 v3 pith:KADNOAG3 submitted 2019-07-02 math.PR

Xinxing Chen , Victor Dagard , Bernard Derrida , Yueyun Hu , Mikhail Lifshits , Zhan Shi This is my paper · ORCID
classification math.PR
keywords conjecturederridaintegrabilitymodelsrecursiveretauxanswerassumption
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abstract

We are interested in the nearly supercritical regime in a family of max-type recursive models studied by Collet, Eckman, Glaser and Martin and 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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