Abstract
This paper establishes necessary and sufficient conditions for the sequence of products of freely independent unitary operators to converge in distribution to the uniform law on the unit circle.
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The author would like to express his gratitude to Diana Bloom for her help with editing, and to Professor Raghu Varadhan for useful discussions.
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Kargin, V. A limit theorem for products of free unitary operators. Probab. Theory Relat. Fields 141, 603–623 (2008). https://doi.org/10.1007/s00440-007-0095-9
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DOI: https://doi.org/10.1007/s00440-007-0095-9
Keywords
- Free probability
- Free multiplicative convolution
- Unitary operators
- Limit theorem
Mathematics Subject Classification (2000)
- 46L53
- 46L54
- 60F05