Invasion percolation and critical transient in the Barabasi model of human dynamics

被引：37
作者：
Gabrielli, A.
Caldarelli, G.
机构：
[1] Univ Roma La Sapienza, Dipartimento Fis, CNR, INFM,SMC, I-00185 Rome, Italy
[2] CNR, Ist Sistemi Complessi, I-00185 Rome, Italy
来源：
PHYSICAL REVIEW LETTERS | 2007年 / 98卷 / 20期
关键词：
D O I：
10.1103/PhysRevLett.98.208701
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We introduce an exact probabilistic description for L=2 of the Barabasi model for the dynamics of a list of L tasks. This permits us to study the problem out of the stationary state and to solve explicitly the extremal limit case where a critical behavior for the waiting time distribution is observed. This behavior deviates at any finite time from that of the stationary state. We study also the characteristic relaxation time for finite time deviations from stationarity in all cases showing that it diverges in the extremal limit, confirming that these deviations are important at all time.
引用
收藏
页数：4
相关论文
共 13 条
[1]   The origin of bursts and heavy tails in human dynamics [J].
Barabási, AL .
NATURE, 2005, 435 (7039) :207-211
[2]  
Breuer L., 2005, An Introduction to Queueing Theory and Matrix-Analytic Methods
[3]   Theory of extremal dynamics with quenched disorder: Invasion percolation and related models [J].
Cafiero, R ;
Gabrielli, A ;
Marsili, M ;
Pietronero, L .
PHYSICAL REVIEW E, 1996, 54 (02) :1406-1425
[4]   Perturbative approach to the Bak-Sneppen model [J].
Felici, M ;
Caldarelli, G ;
Gabrielli, A ;
Pietronero, L .
PHYSICAL REVIEW LETTERS, 2001, 86 (09) :1896-1899
[5]   Invasion percolation with temperature and the nature of self-organized criticality in real systems [J].
Gabrielli, A ;
Caldarelli, G ;
Pietronero, L .
PHYSICAL REVIEW E, 2000, 62 (06) :7638-7641
[6]   Comment on the run time statistics in models of growth in disordered media [J].
Gabrielli, A ;
Marsili, M ;
Cafiero, R ;
Pietronero, L .
JOURNAL OF STATISTICAL PHYSICS, 1996, 84 (3-4) :889-893
[7]   Biased diffusion and universality in model queues [J].
Grinstein, G. ;
Linsker, R. .
PHYSICAL REVIEW LETTERS, 2006, 97 (13)
[8]   RUN-TIME STATISTICS IN MODELS OF GROWTH IN DISORDERED MEDIA [J].
MARSILI, M .
JOURNAL OF STATISTICAL PHYSICS, 1994, 77 (3-4) :733-754
[9]   Human dynamics:: Darwin and Einstein correspondence patterns [J].
Oliveira, JG ;
Barabási, AL .
NATURE, 2005, 437 (7063) :1251-1251
[10]  
Tijms H.C., 2003, A first course in stochastic models
12