Some Results on the Distributions of Operator Valued Semicircular Random Variables
| dc.contributor.advisor | Belinschi, Serban | en_US |
| dc.contributor.advisor | Samei, Ebrahim | en_US |
| dc.contributor.committeeMember | Steel, Tom | en_US |
| dc.contributor.committeeMember | Choi, Yemon | en_US |
| dc.contributor.committeeMember | Soteros, Chris | en_US |
| dc.creator | Soltanifar, Mohsen | en_US |
| dc.date.accessioned | 2013-01-03T22:33:43Z | |
| dc.date.available | 2013-01-03T22:33:43Z | |
| dc.date.created | 2011-08 | en_US |
| dc.date.issued | 2011-09-13 | en_US |
| dc.date.submitted | August 2011 | en_US |
| dc.description.abstract | The operator-valued free central limit theorem and operator-valued semi-circular random variables were first introduced by D. Voiculescu in 1995 as operator-valued free analogues of the classical central limit theorem and normal random variables, respectively. In 2007, R. Speicher and others showed that the operator-valued Cauchy transform of the semicircular distribution satisfies a functional equation involving the variance of the semicircular distribution. In this thesis, we consider a non - commutative probability space (A,EB,B) where in which A is a unital C*-algebra, B is a C*-subalgebra of A containing its unit and EB: A → B is a conditional expectation. For a given B−valued self-adjoint semicircular random variable S ∈ A with variance η, it is still an open question under what conditions the distribution of S has an atomic part. We provide a partial answer in terms of properties of η when B is the algebra of n × n complex matrices. In addition, we show that for a given compactly supported probability measure its associated Cauchy transform can be represented in terms of the operator-valued Cauchy transforms of a sequence of finite dimensional matrix-valued semicircular random variables in two ways. Finally, we give another representation of its Cauchy transform in terms of operator-valued Cauchy transform of an in finite dimensional matrix-valued semicircular random variable. | en_US |
| dc.identifier.uri | http://hdl.handle.net/10388/ETD-2011-08-60 | en_US |
| dc.language.iso | eng | en_US |
| dc.subject | Semicircular distributions, Atoms, Cauchy transform, Continued Fraction | en_US |
| dc.title | Some Results on the Distributions of Operator Valued Semicircular Random Variables | en_US |
| dc.type.genre | Thesis | en_US |
| dc.type.material | text | en_US |
| thesis.degree.department | Mathematics and Statistics | en_US |
| thesis.degree.discipline | Mathematics | en_US |
| thesis.degree.grantor | University of Saskatchewan | en_US |
| thesis.degree.level | Masters | en_US |
| thesis.degree.name | Master of Science (M.Sc.) | en_US |