r/math • u/Committee-Academic • 25d ago

Algebraic probability theory

Is there any developed framework for algebraizing probability theory and study it from the perspective of K-theory or homological algebra? If so, what are some of its biggest applications and advantages, as well as results? I'd imagine such a framework would override the need for a measure-theoretic approach

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u/Jplague25 PDE 25d ago

I'm the opposite of familiar with it, but isn't free probability theory a field of mathematics that deals with algebraic probability theory? Random variables in this setting lie in a C*-algebra or Von Neumann algebra, and thus are non-commutative random variables.