THE DERRIDA-RETAUX CONJECTURE ON RECURSIVE MODELS

• 成果类型: Article
• 署名作者: Chen, Xinxing; Dagard, Victor; Derrida, Bernard; Hu, Yueyun; Lifshits, Mikhail; Shi, Zhan
• 署名单位: Shanghai Jiao Tong University; Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Cite; Universite PSL; College de France; Saint Petersburg State University; Sorbonne Universite; Universite Paris Cite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1457
• 发表日期: 2021
• 页码: 637-670
• 关键词: iterated functions; spin-glass; disorder

摘要

We are interested in the nearly supercritical regime in a family of maxtype recursive models studied by Collet, Eckman, Glaser and Martin (Comm. Math. Phys. 94 (1984) 353-370) and by Derrida and Retaux (J. Stat. Phys. 156 (2014) 268-290) 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 12. This gives a weaker answer to a conjecture of Derrida and Retaux (J. Stat. Phys. 156 (2014) 268-290). Other behaviours are obtained when the integrability condition is not satisfied.