Cumulants in Noncommutative Probability Theory IV. De Finetti's Theorem and $L^p$-Inequalities

Franz Lehner

doi:10.1016/j.jfa.2006.06.005

Cumulants in Noncommutative Probability Theory IV. De Finetti's Theorem and $L^p$-Inequalities

Operator Algebras 2013-12-20 v2 Combinatorics

Authors: Franz Lehner

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Abstract

In this paper we collect a few results about exchangeability systems in which crossing cumulants vanish, which we call noncrossing exchangeability systems. The main result is a free version of De Finetti's theorem, characterising amalgamated free products as noncrossing exchangeability systems which satisfy a so-called weak singleton condition. The main tool in the proof is an $L^p$ -inequality with uniformly bounded constants for i.i.d. sequences in noncrossing exchangeability systems.

Keywords

noncommutative probability cumulants exchangeability systems de finetti theorem free products l^p-inequalities

Cite

@article{arxiv.math/0409025,
  title  = {Cumulants in Noncommutative Probability Theory IV. De Finetti's Theorem and $L^p$-Inequalities},
  author = {Franz Lehner},
  journal= {arXiv preprint arXiv:math/0409025},
  year   = {2013}
}

Comments

33 pages, AMS LaTeX; Brillinger's formula transferred to separate paper

Cumulants in Noncommutative Probability Theory IV. De Finetti's Theorem and $L^p$-Inequalities

Abstract

Keywords

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