The Derrida--Retaux conjecture on recursive models
Probability
2020-05-05 v3
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 . This gives a weaker answer to a conjecture of Derrida and Retaux. Other behaviours are obtained when the integrability condition is not satisfied.
Cite
@article{arxiv.1907.01601,
title = {The Derrida--Retaux conjecture on recursive models},
author = {Xinxing Chen and Victor Dagard and Bernard Derrida and Yueyun Hu and Mikhail Lifshits and Zhan Shi},
journal= {arXiv preprint arXiv:1907.01601},
year = {2020}
}
Comments
revised version with additional explanations of the techniques; some citations are modified