Open Markov Processes

I gave a talk on some work I did with Kenny Courser. You can see slides of the talk, and also a video and the papers it’s based on:

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.

2 Responses to Open Markov Processes

  1. […] Open Markov Processes ( […]

  2. My student Kenny Courser‘s thesis has hit the arXiv:

    • Kenny Courser, Open Systems: A Double Categorical Perspective, Ph.D. thesis, U. C. Riverside, 2020.

You can use Markdown or HTML in your comments. You can also use LaTeX, like this: $latex E = m c^2 $. The word 'latex' comes right after the first dollar sign, with a space after it.

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.