A Max-Type Recursive Model: Some Properties and Open Questions

  • Xinxing Chen
  • Bernard Derrida
  • Yueyun Hu
  • Mikhail Lifshits
  • Zhan ShiEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 300)


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 critical regime, for which we study the extinction probability, the first moment and the moment generating function. Several stronger assertions are stated as conjectures.


Max-type recursive model Critical regime Free energy Survival probability 



X. C. was supported by NSFC grants Nos. 11771286 and 11531001. M. L. was supported by RFBR grant 16-01-00258. Part of the work was carried out when M. L. and Z. S. were visiting, respectively, LPMA Université Pierre et Marie Curie in June and July 2016, and New York University Shanghai in spring 2016; we are grateful to LPMA and NYUSH for their hospitality.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Xinxing Chen
    • 1
  • Bernard Derrida
    • 2
    • 3
  • Yueyun Hu
    • 4
  • Mikhail Lifshits
    • 5
    • 6
  • Zhan Shi
    • 7
    Email author
  1. 1.School of Mathematical SciencesShanghai Jiaotong UniversityShanghaiChina
  2. 2.Collège de FranceParis Cedex 05France
  3. 3.Laboratoire de Physique Statistique, École Normale SupérieureUniversité Pierre et Marie Curie, Université Denis Diderot, CNRSParis Cedex 05France
  4. 4.LAGA, Université Paris XIIIVilletaneuseFrance
  5. 5.St. Petersburg State UniversitySt. PetersburgRussia
  6. 6.MAI, Linköping UniversityLinköpingSweden
  7. 7.LPMA, Université Pierre et Marie CurieParis Cedex 05France

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