On the genealogy of branching random walks and of directed polymers

被引：15
|
作者：
Derrida, Bernard [1 ,2 ]
Mottishaw, Peter [3 ]
机构：
[1] Coll France, 11 Pl Marcelin Berthelot, F-75005 Paris, France
[2] Ecole Normale Super, LPS, 24 Rue Lhomond, F-75005 Paris, France
[3] Univ Edinburgh, Sch Phys & Astron, James Clerk Maxwell Bldg,Peter Guthrie Tait Rd, Edinburgh EH9 3FD, Midlothian, Scotland
来源：
EPL | 2016年 / 115卷 / 04期
关键词：
REPLICA SYMMETRY-BREAKING; TRAVELING-WAVES; DISORDERED TREES; BROWNIAN-MOTION; SPIN-GLASSES; FLUCTUATIONS; ENERGY; DIMENSIONS; MODEL;
D O I：
10.1209/0295-5075/115/40005
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
It is well known that the mean-field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite-size correction to this distribution of overlaps has a universal character which can be computed explicitly. Our results can also be interpreted as genealogical properties of branching Brownian motion or of branching random walks. Copyright (C) EPLA, 2016
引用
收藏
页数：7
相关论文
共 50 条
  • [1] MINIMAL POSITION AND CRITICAL MARTINGALE CONVERGENCE IN BRANCHING RANDOM WALKS, AND DIRECTED POLYMERS ON DISORDERED TREES
    Hu, Yueyun
    Shi, Zhan
    ANNALS OF PROBABILITY, 2009, 37 (02): : 742 - 789
  • [2] Global survival of branching random walks and tree-like branching random walks
    Bertacchi, Daniela
    Coletti, Cristian F.
    Zucca, Fabio
    ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2017, 14 (01): : 381 - 402
  • [3] Branching Random Walks and Martingales
    Shi, Zhan
    BRANCHING RANDOM WALKS: ECOLE D'ETE DE PROBABILITES DE SAINT-FLOUR XLII - 2012, 2015, 2151 : 19 - 28
  • [4] Cookie branching random walks
    Bartsch, Christian
    Kochler, Michael
    Kochler, Thomas
    Mueller, Sebastian
    Popov, Serguei
    ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2013, 10 (01): : 323 - 358
  • [5] On the trace of branching random walks
    Benjamini, Itai
    Mueller, Sebastian
    GROUPS GEOMETRY AND DYNAMICS, 2012, 6 (02) : 231 - 247
  • [6] Branching Random Walks with Selection
    Shi, Zhan
    BRANCHING RANDOM WALKS: ECOLE D'ETE DE PROBABILITES DE SAINT-FLOUR XLII - 2012, 2015, 2151 : 99 - 105
  • [7] MINIMA IN BRANCHING RANDOM WALKS
    Addario-Berry, Louigi
    Reed, Bruce
    ANNALS OF PROBABILITY, 2009, 37 (03): : 1044 - 1079
  • [8] Simplicial branching random walks
    Rosenthal R.
    Journal of Applied and Computational Topology, 2024, 8 (6) : 1751 - 1791
  • [9] Directed random walks on hierarchical trees with continuous branching: A renormalization group approach
    Saakian, David B.
    PHYSICAL REVIEW E, 2012, 85 (01):
  • [10] The calculation of multifractal properties of directed random walks on hierarchic trees with continuous branching
    Saakian, David B.
    JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2012,
12345