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arXiv · 1907.01601

The Derrida--Retaux conjecture on recursive models

Xinxing Chen·Victor Dagard·Bernard Derrida·Yueyun Hu·Mikhail Lifshits·Zhan Shi
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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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Xinxing Chen, Victor Dagard, Bernard Derrida, Yueyun Hu, Mikhail Lifshits, Zhan Shi. 2020-05-03. The Derrida--Retaux conjecture on recursive models. https://arxiv.org/abs/1907.01601

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