Open Markov Processes

I’m giving a talk on work done with Kenny Courser. It’s part of the ACT2020 conference, and it’s happening on 20:40 UTC on Tuesday July 7th, 2020. (That’s 1:40 pm here in California, just so I don’t forget.)

Like all talks at this conference, you can watch it live on Zoom or on YouTube. It’ll also be recorded, so you can watch it later on YouTube too, somewhere here.

You can see my slides now, and read some other helpful things:

• Coarse-graining open Markov processes.

Abstract. We illustrate some new paradigms in applied category theory with the example of coarse-graining open Markov processes. Coarse-graining is a standard method of extracting a simpler Markov process from a more complicated one by identifying states. Here we extend coarse-graining to ‘open’ Markov processes: that is, those where probability can flow in or out of certain states called ‘inputs’ and ‘outputs’. One can build up an ordinary Markov process from smaller open pieces in two basic ways: composition, where we identify the outputs of one open Markov process with the inputs of another, and tensoring, where we set two open Markov processes side by side. These constructions make open Markov processes into the morphisms of a symmetric monoidal category. But we can go further and construct a symmetric monoidal double category where the 2-morphisms include ways of coarse-graining open Markov processes. We can describe the behavior of open Markov processes using double functors out of this double category.

For more, look at these:

• John Baez, Brendan Fong and Blake Pollard, A compositional framework for Markov processes. (Blog article here.)

• John Baez and Kenny Courser, Coarse-graining open Markov processes. (Blog article here.)

• Kenny Courser, Open Systems: A Double Categorical Perspective.