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The dual Derrida–Retaux conjecture

Author

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  • Chen, Xinxing
  • Hu, Yueyun
  • Shi, Zhan

Abstract

We consider a recursive system (Xn) which was introduced by Collet et al. (1984)) as a spin glass model, and later by Derrida et al. (1992) and by Derrida and Retaux (2014) as a simplified hierarchical renormalization model. The system (Xn) is expected to possess highly nontrivial universalities at or near criticality. In the nearly supercritical regime, Derrida and Retaux (2014) conjectured that the free energy of the system decays exponentially with exponent (p−pc)−12 as p↓pc. We are interested in the nearly subcritical regime (p↑pc), and study a dual version of the Derrida–Retaux conjecture.

Suggested Citation

  • Chen, Xinxing & Hu, Yueyun & Shi, Zhan, 2024. "The dual Derrida–Retaux conjecture," Stochastic Processes and their Applications, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:spapps:v:171:y:2024:i:c:s0304414924000383
    DOI: 10.1016/j.spa.2024.104332
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