The mathematical axiomatics of quantum mechanics leads to the emergence of a new mathematical discipline – noncommutative probability theory. With this approach random variables are determined by positive operator-valued measures and expectations are given by positive functionals on the algebra of all bounded operators. At the same time, the properties of variances and covariances in noncommutative probability theory turn out to be different from their classical counterparts.

Financial support. The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2022-265).

Lecturer
Amosov Grigori Gennadievich

Organizations
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center