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

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.

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Franz Lehner. 2013-12-19. Cumulants in Noncommutative Probability Theory IV. De Finetti's Theorem and $L^p$-Inequalities. https://doi.org/10.1016/j.jfa.2006.06.005

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