Limit Theorems for Non-Commutative Random Variables |
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Authors: | Email author" target="_blank">A?Coja-OghlanEmail author J?Michali?ek |
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Institution: | (1) Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany;(2) Mathematisches Seminar, Universität Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany |
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Abstract: | We study the weak law of large numbers and the central limit theorem for non-commutative random variables. We first define the concepts of variance and expectation for probability measures on homogeneous spaces, and formulate the weak law of large numbers and the central limit theorem for probability measures on locally compact groups. Then, we consider the non-commutative case, where the homogeneous space is replaced by a C*-algebra
that is equipped with a locally compact group G of automorphisms. We define the concepts of variance and expectation in the non-commutative situation. Furthermore, we prove that the weak law of large numbers and the central limit theorem hold for non-commutative random variables on
if they hold on the group G of automorphisms. |
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Keywords: | C*-algebras non-commutative probability theory central limit theorem law of large numbers |
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