Boundary rules and breaking of self-organized criticality in 2D frozen percolation

被引：2
|
作者：
van den Berg, Jacob [1 ,2 ]
Nolin, Pierre [3 ]
机构：
[1] CWI, Amsterdam, Netherlands
[2] Vrije Univ Amsterdam, Amsterdam, Netherlands
[3] City Univ Hong Kong, Kowloon, Hong Kong, Peoples R China
来源：
ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2017年 / 22卷
关键词：
frozen percolation; near-critical percolation; self-organized criticality; BROWNIAN INTERSECTION EXPONENTS; NEAR-CRITICAL PERCOLATION; INVASION PERCOLATION; PLANE EXPONENTS; SCALING LIMITS; DIMENSIONS; CLUSTERS; VALUES;
D O I：
10.1214/17-ECP98
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：
We study frozen percolation on the (planar) triangular lattice, where connected components stop growing ("freeze") as soon as their "size" becomes at least N, for some parameter N >= 1. The size of a connected component can be measured in several natural ways, and we consider the two particular cases of diameter and volume (i.e. number of sites). Diameter-frozen and volume-frozen percolation have been studied in previous works ([5, 15] and [6, 4], resp.), and they display radically different behaviors. These works adopt the rule that the boundary of a frozen cluster stays vacant forever, and we investigate the influence of these "boundary rules" in the present paper. We prove the (somewhat surprising) result that they strongly matter in the diameter case, and we discuss briefly the volume case.
引用
收藏
页数：15
相关论文
共 50 条
  • [31] Seismicity and self-organized criticality
    Turcotte, DL
    PHYSICS OF THE EARTH AND PLANETARY INTERIORS, 1999, 111 (3-4) : 275 - 293
  • [32] Self-organized criticality and earthquakes
    Caruso, Filippo
    Pluchino, Alessandro
    Latora, Vito
    Rapisarda, Andrea
    Vinciguerra, Sergio
    COMPLEXITY, METASTABILITY AND NONEXTENSIVITY, 2007, 965 : 281 - +
  • [33] SELF-ORGANIZED CRITICALITY AND EARTHQUAKES
    SORNETTE, A
    SORNETTE, D
    EUROPHYSICS LETTERS, 1989, 9 (03): : 197 - 202
  • [34] Proof of breaking of self-organized criticality in a nonconservative Abelian sandpile model
    Tsuchiya, T
    Katori, M
    PHYSICAL REVIEW E, 2000, 61 (02): : 1183 - 1188
  • [35] Proof of breaking of self-organized criticality in a nonconservative Abelian sandpile model
    Tsuchiya, Tomoko
    Katori, Makoto
    Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2000, 61 (02): : 1183 - 1188
  • [36] CASCADES AND SELF-ORGANIZED CRITICALITY
    MANNA, SS
    KISS, LB
    KERTESZ, J
    JOURNAL OF STATISTICAL PHYSICS, 1990, 61 (3-4) : 923 - 932
  • [37] Turbulent self-organized criticality
    De Menech, M
    Stella, AL
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2002, 309 (3-4) : 289 - 296
  • [38] SIMULATION OF SELF-ORGANIZED CRITICALITY
    BAK, P
    PHYSICA SCRIPTA, 1990, T33 : 9 - 10
  • [39] Apparent self-organized criticality
    Tainaka, Kei-Ichi
    Itoh, Yoshiaki
    Physics Letters, Section A: General, Atomic and Solid State Physics, 1996, 220 (1-3): : 58 - 62
  • [40] Self-organized criticality paradigm
    Duran, I
    Stöckel, J
    Hron, M
    Horácek, J
    Jakubka, K
    Kryska, L
    CZECHOSLOVAK JOURNAL OF PHYSICS, 2000, 50 : 42 - 46
12345