University of Connecticut

Analysis Learning Seminar


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Title: Algebraic Probability and Stochastic Processes I
Speaker: Arthur Parzygnat (University of Connecticut)
Time: Friday, March 24, 2017 at 3:30 pm
Place: MONT 313Abstract: Certain algebraic structures reproduce familiar notions from probability theory. These are states on C∗-algebras and completely positive maps between them. In the case of commutative algebras, these reproduce spaces with probability density functions and stochastic processes between them. The non-commutative analogues can be interpreted as non-commutative probability theory. To set the stage, the first lecture is about finite probability spaces, stochastic matrices, and their algebraic analogues. In the second lecture, we discuss the Gelfand-Naimark Theorem, which provides an equivalence between commutative C∗-algebras and compact Hausdorff topological spaces. In the third lecture, we come back to studying states on arbitrary (not necessarily finite-dimensional) commutative C∗-algebras. Occasional references will be made to quantum mechanics.

Organizer: Matthew Badger