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 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 $\frac{1}{2}$. This gives a weaker answer to a conjecture of Derrida and Retaux. Other behaviours are obtained when the integrability condition is not satisfied.

arXiv commentrevised version with additional explanations of the techniques; some citations are modified

References in corpus (5)

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Cited by in corpus (3)

• Localization, big-jump regime and the effect disorder for a class of generalized pinning models
• Results and conjectures on a toy model of depinning
• Parking on Cayley trees & Frozen Erdös-Rényi