Hoeffding spaces and Specht modules

Giovanni Peccati; Jean-Renaud Pycke

ESAIM: Probability and Statistics (2011)

  • Volume: 15, page S58-S68
  • ISSN: 1292-8100

Abstract

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It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module.

How to cite

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Peccati, Giovanni, and Pycke, Jean-Renaud. "Hoeffding spaces and Specht modules." ESAIM: Probability and Statistics 15 (2011): S58-S68. <http://eudml.org/doc/197767>.

@article{Peccati2011,
abstract = { It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module. },
author = {Peccati, Giovanni, Pycke, Jean-Renaud},
journal = {ESAIM: Probability and Statistics},
keywords = {Exchangeability; finite population statistics; Hoeffding decompositions; irreducible representations; random permutations; Specht modules; symmetric group},
language = {eng},
month = {5},
pages = {S58-S68},
publisher = {EDP Sciences},
title = {Hoeffding spaces and Specht modules},
url = {http://eudml.org/doc/197767},
volume = {15},
year = {2011},
}

TY - JOUR
AU - Peccati, Giovanni
AU - Pycke, Jean-Renaud
TI - Hoeffding spaces and Specht modules
JO - ESAIM: Probability and Statistics
DA - 2011/5//
PB - EDP Sciences
VL - 15
SP - S58
EP - S68
AB - It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module.
LA - eng
KW - Exchangeability; finite population statistics; Hoeffding decompositions; irreducible representations; random permutations; Specht modules; symmetric group
UR - http://eudml.org/doc/197767
ER -

References

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  8. G.D. James, The representation theory of the symmetric groups. Lecture Notes in Math.682, Springer-Verlag, Berlin-Heidelberg-New York (1978).  Zbl0393.20009
  9. G. Peccati, Hoeffding-ANOVA decompositions for symmetric statistics of exchangeable observations. Ann. Probab.32 (2004) 1796–1829.  Zbl1055.62060
  10. G. Peccati and J.-R. Pycke, Decompositions of stochastic processes based on irreducible group representations. Theory Probab. Appl.54 (2010) 217–245.  Zbl1229.60039
  11. B.E. Sagan, The Symmetric Group. Representations, Combinatorial Algorithms and Symmetric Functions, 2nd edition. Springer, New York (2001).  Zbl0964.05070
  12. R.J. Serfling, Approximation Theorems of Mathematical Statistics. Wiley, New York (1980).  Zbl0538.62002
  13. J.-P. Serre, Linear representations of finite groups, Graduate Texts Math.42, Springer, New York (1977).  
  14. L. Zhao and X. Chen, Normal approximation for finite-population U-statistics. Acta Math. Appl. Sinica6 (1990) 263–272.  Zbl0724.60024

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