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# Blog - network theory (part 23)

In this post:

I'll show how any graph with positive numbers attached to its edges gives a Markov process, and write down a nice formula for the Hamiltonian of this Markov process:

$$H = \partial s^\dagger$$ Then I'll classify the equilibria of this process, at least when the graph is 'weakly reversible'. This is yet another step toward proving the zero deficiency theorem.

So far this article is just a stub... I'll let you know when I write enough to be interesting!

## Comments

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1.
edited August 2012

Well, I'm done with

now!

The first theorem here must be incredibly well-known - it's a basic fact about Markov processes. When I write the book, I'll push this much earlier, so I can just use it here. It's interesting in its own right, but getting it done sooner will make the proof of the deficiency zero theorem a lot easier to follow. I feel I'm just learning now how the whole series should have been written.

Comment Source:Well, I'm done with * [[Blog - network theory (part 23)]] now! The first theorem here must be incredibly well-known - it's a basic fact about Markov processes. When I write the book, I'll push this much earlier, so I can just _use_ it here. It's interesting in its own right, but getting it done sooner will make the proof of the deficiency zero theorem a lot easier to follow. I feel I'm just learning now how the whole series should have been written.
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