Two particles' repelling random walks on the complete graph

被引：2
作者：
Chen, Jun [1 ]
机构：
[1] CALTECH, Div Humanities & Social Sci, Pasadena, CA 91125 USA
来源：
ELECTRONIC JOURNAL OF PROBABILITY | 2014年 / 19卷
关键词：
Repelling random walks; Reinforced random walk; multi-particle; complete graph; stochastic approximation algorithms; dynamical approach; chain recurrent set; Lyapunov function; REINFORCED-RANDOM-WALK; STOCHASTIC APPROXIMATIONS; ATTRACTING EDGE; POINTS;
D O I：
10.1214/EJP.v19-2669
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 consider two particles' repelling random walks on complete graphs. In this model, each particle has higher probability to visit the vertices which have been seldom visited by the other one. By a dynamical approach we prove that the two particles' occupation measure asymptotically has small joint support almost surely if the repulsion is strong enough.
引用
收藏
页数：17
相关论文
共 50 条
  • [31] Two Algorithms for Computing All Spanning Trees of a Simple, Undirected, and Connected Graph: Once Assuming a Complete Graph
    Chakraborty, Maumita
    Chowdhury, Sumon
    Pal, Rajat K.
    IEEE ACCESS, 2018, 6 : 56290 - 56300
  • [32] Decomposition of the line graph of the complete graph into stars
    Xin, Yue
    Yang, Weihua
    DISCRETE MATHEMATICS, 2024, 347 (07)
  • [33] Completely disconnecting the complete graph
    Ginsburg, J
    Sands, B
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2000, 13 (01) : 33 - 47
  • [34] Asymptotics for push on the complete graph
    Daknama, Rami
    Panagiotou, Konstantinos
    Reisser, Simon
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2021, 137 : 35 - 61
  • [35] On recurrence and transience of self-interacting random walks
    Yuval Peres
    Serguei Popov
    Perla Sousi
    Bulletin of the Brazilian Mathematical Society, New Series, 2013, 44 : 841 - 867
  • [36] A connection between a system of random walks and rumor transmission
    Lebensztayn, E.
    Rodriguez, P. M.
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2013, 392 (23) : 5793 - 5800
  • [37] Asymptotics for pull on the complete graph
    Panagiotou, Konstantinos
    Reisser, Simon
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2023, 159 : 541 - 563
  • [38] Fault Diameter of Strong Product Graph of an Arbitrary Connected Graph and a Complete Graph
    Yue, Yuxiang
    Li, Feng
    ENGINEERING LETTERS, 2024, 32 (04) : 800 - 805
  • [39] Periodicity of Grover walks on complete graphs with self-loops
    Ito, Naoharu
    Matsuyama, Toyoki
    Tsurii, Tatsuya
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2020, 599 (599) : 121 - 132
  • [40] Long Term Behaviour of a Reversible System of Interacting Random Walks
    Janson, Svante
    Shcherbakov, Vadim
    Volkov, Stanislav
    JOURNAL OF STATISTICAL PHYSICS, 2019, 175 (01) : 71 - 96
12345