The sustainability probability for the critical Derrida-Retaux model

• 成果类型: Article
• 署名作者: Chen, Xinxing; Hu, Yueyun; Shi, Zhan
• 署名单位: Shanghai Jiao Tong University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-021-01091-z
• 发表日期: 2022
• 页码: 641-684
• 关键词: iterated functions; spin-glass; disorder

摘要

We are interested in the recursive model (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). We prove that at criticality, the probability P(Y-n > 0) behaves like n(-2+o(1)) as n goes to infinity; this gives a weaker confirmation of predictions made in Collet et al. (1984), Derrida and Retaux (2014) and Chen et al. (in: Sidoravicius (ed) Sojourns in probability theory and statistical physics-III, Springer, Singapore, 2019). Our method relies on studying the number of pivotal vertices and open paths, combined with a delicate coupling argument.