2020-11-05: Eigil Rischel (MSP)

Tue, 14 Oct 2025 16:51:42 +0000

Eigil Rischel (MSP)

Probability theory with string diagrams

Abstract

Going back to Lawvere, people have tried to study probability theory in terms of monads - the idea being that for each "space" of some type, X, there should be a space PX of probability distributions on X, with point-distributions and integration of distributions giving the monad structure. The Kleisli category of this monad is of particular interest: it corresponds to "stochastic maps" between spaces.

It turns out that one can actually often do without the monad - the Kleisli category itself carries enough structure that one can do probability theory "internally", rederiving the notions of determinism, independence of measures, and many others. I will present this picture of probability, and give some examples of results that can be proven in this framework.

2020-11-05 13:00:00 UTC
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