CENTRAL LIMIT THEOREMS FOR PATTERNS IN MULTISET PERMUTATIONS AND SET PARTITIONS

被引：5
|
作者：
Feray, Valentin [1 ]
机构：
[1] Univ Zurich, Inst Math, Zurich, Switzerland
来源：
ANNALS OF APPLIED PROBABILITY | 2020年 / 30卷 / 01期
基金：
瑞士国家科学基金会;
关键词：
Combinatorial probability; central limit theorem; dependency graphs; patterns; multi-set permutations; set partitions; PROBABILITY; NUMBER; OCCURRENCES; STATISTICS; BEHAVIOR; SUMS;
D O I：
10.1214/19-AAP1502
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 use the recently developed method of weighted dependency graphs to prove central limit theorems for the number of occurrences of any fixed pattern in multiset permutations and in set partitions. This generalizes results for patterns of size 2 in both settings, obtained by Canfield, Janson and Zeil-berger and Chern, Diaconis, Kane and Rhoades, respectively.
引用
收藏
页码：287 / 323
页数：37
相关论文
共 50 条
  • [41] RANDOM CENTRAL LIMIT THEOREMS FOR MARTINGALES
    RAO, BLS
    [J]. ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1969, 20 (1-2): : 217 - &
  • [42] Central limit theorems for random polytopes
    Matthias Reitzner
    [J]. Probability Theory and Related Fields, 2005, 133 : 483 - 507
  • [43] Irregular sets and central limit theorems
    Perera, G
    [J]. BERNOULLI, 2002, 8 (05) : 627 - 642
  • [44] Non-central Limit Theorems
    Major, Peter
    [J]. MULTIPLE WIENER-ITO INTEGRALS: WITH APPLICATIONS TO LIMIT THEOREMS, 2ND EDITION, 2014, 849 : 87 - 112
  • [45] NEW CONDITIONS FOR CENTRAL LIMIT THEOREMS
    PIERRE, PA
    [J]. ANNALS OF MATHEMATICAL STATISTICS, 1969, 40 (01): : 319 - &
  • [46] Limit theorems for patterns in phylogenetic trees
    Chang, Huilan
    Fuchs, Michael
    [J]. JOURNAL OF MATHEMATICAL BIOLOGY, 2010, 60 (04) : 481 - 512
  • [47] CENTRAL LIMIT THEOREMS FOR MULTINOMIAL SUMS
    MORRIS, C
    [J]. ANNALS OF STATISTICS, 1975, 3 (01): : 165 - 188
  • [48] Central limit theorems for urn models
    Smythe, RT
    [J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1996, 65 (01) : 115 - 137
  • [49] CENTRAL-LIMIT THEOREMS ON GROUPS
    MELLO, PA
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 1986, 27 (12) : 2876 - 2891
  • [50] CENTRAL LIMIT THEOREMS IN THE CONFIGURATION MODEL
    Barbour, A. D.
    Rollin, Adrian
    [J]. ANNALS OF APPLIED PROBABILITY, 2019, 29 (02): : 1046 - 1069
12345