A quadratic regression problem for two-state algebras with application to the Central Limit Theorem
Marek Bozejko, Wlodzimierz Bryc
TL;DR
This paper extends a free probability version of the Laha-Lukacs theorem to two-state probability spaces and applies it to generalize a noncommutative Central Limit Theorem to this setting.
Contribution
It introduces a quadratic regression problem for two-state algebras and generalizes the noncommutative CLT to two-state probability spaces.
Findings
Extended free Laha-Lukacs theorem to two-state spaces
Generalized Kargin's noncommutative CLT to two-state setting
Provided new tools for noncommutative probability with two states
Abstract
We extend a free version of the Laha-Lukacs theorem to probability spaces with two-states. We then use this result to generalize a noncommutative CLT of Kargin to the two-state setting.
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Taxonomy
TopicsRandom Matrices and Applications · Matrix Theory and Algorithms · Markov Chains and Monte Carlo Methods