Limit theorems for non-commutative random variables

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Autor/in:
Erscheinungsjahr:
2005
Medientyp:
Text
Schlagworte:
  • C*-algebras
  • Central limit theorem
  • Law of large numbers
  • Non-commutative probability theory
Beschreibung:
  • 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 A 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 A if they hold on the group G of automorphisms. © 2005 Springer Science+Business Media, Inc.
Lizenz:
  • info:eu-repo/semantics/closedAccess
Quellsystem:
Forschungsinformationssystem der UHH
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oai:www.edit.fis.uni-hamburg.de:publications/c82655a6-7e69-489a-aa02-7d3fc89c9ad5