|DATE||November 21 (Wed), 2018|
|INSTITUTE||University of Connecticut|
|TITLE||[Topology Seminar] Using category theory for non-commutative probability|
Classical conditional probabilities and disintegrations can be formulated diagrammatically in a category of stochastic matrices. Combining this with the functor taking stochastic matrices to positive operators on C*-algebras, a notion of non-commutative disintegration and conditional probability can be made for states on C*-algebras. The existence and uniqueness of conditional probabilities is an important fact in probability theory. However, unlike the classical case, the existence of non-commutative disintegrations is not guaranteed even on finite-dimensional matrix algebras. We will state some general existence and uniqueness results as well as illuminating examples. This is joint work with Benjamin P. Russo (Farmingdale State College SUNY).