Hausdorff dimension of random limsup sets

被引：5
|
作者：
Ekstrom, Fredrik [1 ]
Persson, Tomas [1 ]
机构：
[1] Lund Univ, Ctr Math Sci, Box 118, S-22100 Lund, Sweden
来源：
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2018年 / 98卷 / 03期
关键词：
DIOPHANTINE APPROXIMATION; CIRCLE;
D O I：
10.1112/jlms.12158
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove bounds for the almost sure value of the Hausdorff dimension of the limsup set of a sequence of balls in Rd whose centres are independent, identically distributed random variables. The formulas obtained involve the rate of decrease of the radii of the balls and multifractal properties of the measure according to which the balls are distributed, and generalise formulas that are known to hold for particular classes of measures.
引用
收藏
页码：661 / 686
页数：26
相关论文
共 50 条
  • [1] Hausdorff dimension of limsup random fractals
    Zhang, Liang
    [J]. ELECTRONIC JOURNAL OF PROBABILITY, 2013, 18 : 1 - 26
  • [2] HAUSDORFF DIMENSION OF LIMSUP SETS OF RANDOM RECTANGLES IN PRODUCTS OF REGULAR SPACES
    Ekstrom, Fredrik
    Jarvenpaa, Esa
    Jarvenpaa, Maarit
    Suomala, Ville
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146 (06) : 2509 - 2521
  • [3] Dimension of Random Limsup Sets
    Ekstrom, Fredrik
    [J]. AMERICAN MATHEMATICAL MONTHLY, 2019, 126 (09): : 816 - 824
  • [4] HAUSDORFF DIMENSION OF LIMSUP SETS OF RECTANGLES IN THE HEISENBERG GROUP
    Ekstrom, Fredrik
    Jarvenpaa, Esa
    Jarvenpaa, Maarit
    [J]. MATHEMATICA SCANDINAVICA, 2020, 126 (02) : 229 - 255
  • [5] HAUSDORFF DIMENSION OF THE CARTESIAN PRODUCT OF LIMSUP SETS IN DIOPHANTINE APPROXIMATION
    Wang, Baowei
    Wu, Jun
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024,
  • [6] A new Hausdorff content bound for limsup sets
    Eriksson-Bique, Sylvester
    [J]. ADVANCES IN MATHEMATICS, 2024, 445
  • [7] On the Hausdorff Dimension of Some Random Cantor Sets
    V. Paulauskas
    R. Zovė
    [J]. Lithuanian Mathematical Journal, 2003, 43 (2) : 189 - 198
  • [8] Hausdorff dimension of affine random covering sets in torus
    Jarvenpaa, Esa
    Jarvenpaa, Maarit
    Koivusalo, Henna
    Li, Bing
    Suomala, Ville
    [J]. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2014, 50 (04): : 1371 - 1384
  • [9] Hausdorff dimension of invariant sets for random dynamical systems
    Crauel H.
    Flandoli F.
    [J]. Journal of Dynamics and Differential Equations, 1998, 10 (3) : 449 - 474
  • [10] On the Hausdorff dimension of exceptional random sets generated by multivariate spacings
    Coiffard, Claire
    [J]. METRIKA, 2011, 73 (03) : 359 - 371
12345