A survey of one-dimensional random polymers

被引：31
|
作者：
van der Hofstad, R [1 ]
König, W
机构：
[1] Delft Univ Technol, Dept Appl Math, NL-2628 CD Delft, Netherlands
[2] Tech Univ Berlin, Dept Math MA7 5, D-10623 Berlin, Germany
来源：
JOURNAL OF STATISTICAL PHYSICS | 2001年 / 103卷 / 5-6期
关键词：
weakly and strictly self-avoiding walk; polymer measure; large deviation; law of large numbers; central limit theorem; lace expansion;
D O I：
10.1023/A:1010309005541
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In the last decade there has been an enormous progress in the mathematical understanding of one-dimensional polymer measures. which are path measures that suppress self-intersections. We are currently in the situation that many interesting questions have either been answered, or that essential new ideas are needed. In this survey paper, we discuss the most relevant results, open questions, and heuristics.
引用
收藏
页码：915 / 944
页数：30
相关论文
共 50 条
  • [1] A Survey of One-Dimensional Random Polymers
    Remco van der Hofstad
    Wolfgang König
    [J]. Journal of Statistical Physics, 2001, 103 : 915 - 944
  • [2] Weak interaction limits for one-dimensional random polymers
    Remco van der Hofstad
    Frank den Hollander
    Wolfgang König
    [J]. Probability Theory and Related Fields, 2003, 125 : 483 - 521
  • [3] Weak interaction limits for one-dimensional random polymers
    van der Hofstad, R
    den Hollander, F
    König, W
    [J]. PROBABILITY THEORY AND RELATED FIELDS, 2003, 125 (04) : 483 - 521
  • [4] ONE-DIMENSIONAL RANDOM SCHRODINGER-OPERATORS - A SURVEY
    CARMONA, R
    [J]. JOURNAL OF STATISTICAL PHYSICS, 1984, 36 (1-2) : 278 - 278
  • [5] Large deviations for one-dimensional random walk in a random environment - A survey
    Gantert, N
    Zeitouni, O
    [J]. RANDOM WALKS, 1999, 9 : 127 - 165
  • [6] ONE-DIMENSIONAL SCHRODINGER-OPERATORS WITH RANDOM POTENTIALS - A SURVEY
    CARMONA, R
    [J]. ACTA APPLICANDAE MATHEMATICAE, 1985, 4 (01) : 65 - 91
  • [7] One-dimensional polymers in random environments: stretching vs. folding
    Berger, Quentin
    Huang, Chien-Hao
    Torri, Niccolo
    Wei, Ran
    [J]. ELECTRONIC JOURNAL OF PROBABILITY, 2022, 27
  • [8] Bethe ansatz solution for one-dimensional directed polymers in random media
    Dotsenko, Victor
    Klumov, Boris
    [J]. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2010,
  • [9] Polymers as one-dimensional metals
    Troisi, Alessandro
    [J]. NATURE MATERIALS, 2009, 8 (07) : 538 - 539
  • [10] Polymers as one-dimensional metals
    Alessandro Troisi
    [J]. Nature Materials, 2009, 8 : 538 - 539
12345