Asymptotics of variance of the lattice point count

被引：0
|
作者：
Jiří Janáček
机构：
[1] Academy of Sciences of the Czech Republic,Institute of Physiology
来源：
Czechoslovak Mathematical Journal | 2008年 / 58卷
关键词：
point lattice; Fourier transform; volume; variance;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The variance of the number of lattice points inside the dilated bounded set rD with random position in ℝd has asymptotics ∼ rd−1 if the rotational average of the squared modulus of the Fourier transform of the set is O(ϰ−d−1). The asymptotics follow from Wiener’s Tauberian theorem.
引用
收藏
页码：751 / 758
页数：7
相关论文
共 50 条
  • [21] Variance asymptotics and scaling limits for Gaussian polytopes
    Calka, Pierre
    Yukich, J. E.
    PROBABILITY THEORY AND RELATED FIELDS, 2015, 163 (1-2) : 259 - 301
  • [22] Asymptotics of SIMEX-based variance estimation
    Fang, Yun
    Zhu, Li-Xing
    METRIKA, 2012, 75 (03) : 329 - 345
  • [23] Asymptotics of SIMEX-based variance estimation
    Yun Fang
    Li-Xing Zhu
    Metrika, 2012, 75 : 329 - 345
  • [24] Variance asymptotics and scaling limits for random polytopes
    Calka, Pierre
    Yukich, J. E.
    ADVANCES IN MATHEMATICS, 2017, 304 : 1 - 55
  • [25] Variance asymptotics and scaling limits for Gaussian polytopes
    Pierre Calka
    J. E. Yukich
    Probability Theory and Related Fields, 2015, 163 : 259 - 301
  • [26] Random Waves On T3: Nodal Area Variance and Lattice Point Correlations
    Benatar, Jacques
    Maffucci, Riccardo W.
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2019, 2019 (10) : 3032 - 3075
  • [27] A combinatorial understanding of lattice path asymptotics
    Johnson, Samuel
    Mishna, Marni
    Yeats, Karen
    ADVANCES IN APPLIED MATHEMATICS, 2018, 92 : 144 - 163
  • [28] Asymptotics of Superposition of Point Processes
    Decreusefond, L.
    Vasseur, A.
    GEOMETRIC SCIENCE OF INFORMATION, GSI 2015, 2015, 9389 : 187 - 194
  • [29] CORRELATION ASYMPTOTICS FOR A PLANE ISING LATTICE
    RYAZANOV, GV
    SOVIET PHYSICS JETP-USSR, 1966, 22 (04): : 789 - &
  • [30] ON THE SPATIAL ASYMPTOTICS OF SOLUTIONS OF THE TODA LATTICE
    Teschl, Gerald
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2010, 27 (03) : 1233 - 1239
12345