Directed polymers in a random environment: A review of the phase transitions

被引：0
|
作者：
Zygouras, Nikos [1 ]
机构：
[1] Univ Warwick, Dept Math, Coventry CV4 7AL, England
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2024年 / 177卷
基金：
英国工程与自然科学研究理事会;
关键词：
Random polymers; Disordered systems; Phase transitions; Weak and strong disorder; Martingales; Fractional moment method; Coarse graining; Pinning models; Heavy tail disorder; Hierarchical lattices; Intermediate disorder regime; GAUSSIAN MULTIPLICATIVE CHAOS; INTERMEDIATE DISORDER REGIME; STOCHASTIC HEAT-EQUATION; CENTRAL-LIMIT-THEOREM; WALK PINNING MODEL; KPZ EQUATION; CRITICAL-POINTS; WEAK DISORDER; FLUCTUATIONS; LOCALIZATION;
D O I：
10.1016/j.spa.2024.104431
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
The model of directed polymer in a random environment is a fundamental model of interaction between a simple random walk and ambient disorder. This interaction gives rise to complex phenomena and transitions from a central limit theory to novel statistical behaviours. Despite its intense study, there are still many aspects and phases which have not yet been identified. In this review we focus on the current status of our understanding of the transition between weak and strong disorder phases, give an account of some of the methods that the study of the model has motivated and highlight some open questions.
引用
收藏
页数：34
相关论文
共 50 条
12345