The mean square displacement of random walk on the Manhattan lattice

被引：1
|
作者：
Beaton, Nicholas R. [1 ]
Holmes, Mark [1 ]
机构：
[1] Univ Melbourne, Parkville, Vic 3010, Australia
来源：
STATISTICS & PROBABILITY LETTERS | 2023年 / 193卷
关键词：
Manhattan lattice; Random walk; Mean square displacement; CENTRAL-LIMIT-THEOREM;
D O I：
10.1016/j.spl.2022.109706
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 give an explicit formula for the mean square displacement of the random walk on the d-dimensional Manhattan lattice after n steps, for all n and all dimensions d > 2.(c) 2022 Elsevier B.V. All rights reserved.
引用
收藏
页数：5
相关论文
共 50 条
  • [21] ON THE MAXIMAL DISPLACEMENT OF CATALYTIC BRANCHING RANDOM WALK
    Bulinskaya, E., V
    SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2020, 17 : 1088 - 1099
  • [22] MINIMAL DISPLACEMENT OF BRANCHING RANDOM-WALK
    BRAMSON, MD
    ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1978, 45 (02): : 89 - 108
  • [23] Tightness for the minimal displacement of branching random walk
    Bramson, Maury
    Zeitouni, Ofer
    JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2007,
  • [24] A numerical study of Levy random walks: Mean square displacement and power-law propagators
    Trotta, E. M.
    Zimbardo, G.
    JOURNAL OF PLASMA PHYSICS, 2015, 81
  • [25] Self-avoiding walk on a three-dimensional Manhattan lattice
    Fan, K
    Li, XY
    Wu, DC
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2000, 33 (22): : 3971 - 3975
  • [26] The mean square displacement of a ballistic quantum particle
    Bindech, O.
    Gatti, F.
    Mandal, S.
    Marquardt, R.
    Shi, L.
    Tremblay, J. C.
    MOLECULAR PHYSICS, 2024, 122 (15-16)
  • [27] MEAN-SQUARE DISPLACEMENT OF A VIBRATING DISLOCATION
    OHASHI, K
    OHASHI, YH
    PHILOSOPHICAL MAGAZINE A-PHYSICS OF CONDENSED MATTER STRUCTURE DEFECTS AND MECHANICAL PROPERTIES, 1978, 38 (02): : 187 - 204
  • [28] Electrical conductivity and an approximate mean square displacement
    Renato Ribeiro Guimarães
    Denner Serafim Vieira
    Thiago Petrucci
    Hatsumi Mukai
    Paulo Ricardo Garcia Fernandes
    Renio dos Santos Mendes
    Indian Journal of Physics, 2019, 93 : 1437 - 1443
  • [29] Electrical conductivity and an approximate mean square displacement
    Guimaraes, R. R.
    Vieira, D. S.
    Petrucci, T.
    Mukai, H.
    Fernandes, P. R. G.
    Mendes, R. D. S.
    INDIAN JOURNAL OF PHYSICS, 2019, 93 (11) : 1437 - 1443
  • [30] Maximum on a random time interval of a random walk with infinite mean
    Denisov, Denis
    QUEUEING SYSTEMS, 2021, 98 (3-4) : 211 - 223
12345