# The Stable Derrida–Retaux System at Criticality

@article{Chen2020TheSD, title={The Stable Derrida–Retaux System at Criticality}, author={Xinxing Chen and Zhan Shi}, journal={arXiv: Probability}, year={2020} }

The Derrida--Retaux recursive system was investigated by Derrida and Retaux (2014) as a hierarchical renormalization model in statistical physics. A prediction of Derrida and Retaux (2014) on the free energy has recently been rigorously proved (Chen, Dagard, Derrida, Hu, Lifshits and Shi (2019+)), confirming the Berezinskii--Kosterlitz--Thouless-type phase transition in the system. Interestingly, it has been established in Chen, Dagard, Derrida, Hu, Lifshits and Shi (2019+) that the prediction…

## 2 Citations

### The sustainability probability for the critical Derrida–Retaux model

- PhysicsProbability Theory and Related Fields
- 2021

We are interested in the recursive model $$(Y_n, \, n\ge 0)$$ ( Y n , n ≥ 0 ) studied by Collet et al. (Commun Math Phys 94:353–370, 1984) and by Derrida and Retaux (J Stat Phys 156:268–290, 2014).…

### The sustainability probability for the critical Derrida–Retaux model

- Materials ScienceProbability Theory and Related Fields
- 2021

We are interested in the recursive model (Yn,n≥0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}…

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We introduce a toy model, which represents a simplified version of the problem of the depinning transition in the limit of strong disorder. This toy model can be formulated as a simple…

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It is proved that, as soon as disorder is present, the transition is at least of second order, in the sense that the free energy is differentiable at the critical line, so that the order parameter vanishes continuously at the transition.

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For the DNA denaturation transition in the presence of random contact energies, or equivalently the disordered wetting transition, we introduce a strong disorder renewal approach to construct the…

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We review recent results and conjectures for a simplified version of the depinning problem in presence of disorder which was introduced by Derrida and Retaux in 2014. For this toy model, the…

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We consider a simple max-type recursive model which was introduced in the study of depinning transition in presence of strong disorder, by Derrida and Retaux [5]. Our interest is focused on the…

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$$\mathcal{N}[F(s)] = \frac{{(F(s))^2 - (F(0))^2 }}{s} + (F(0))^2 ,$$
with the constraintsF(1)=1,F(s)=∑ansn,an≧0, and find that, except…