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I'm working on a standard problem in random walk in two dimension.

In particular, I'm trying to generate a migration matrix for a toroidal model (Toroidal Transition Matrix) in R.

I have previously posted the same problem here: Transition matrix for a two-dimensional random walk in a torus: compute matrix in R

However, I did not get any feedback.

Similarly to what I mentioned in that post, I decided to assume independent movement along each dimension. Therefore, instead of calculating a Toroidal migration matrix and retrieve transition probabilities, I have multiplied independent probabilities from two separate 'one-dimensional circular model'.

I'm not sure whether this is formally correct and I would like to have some opinion on this regard.

CafféSospeso
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1 Answers1

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Yes, to walk within the torus with each dimension being independent you do just multiply the transition probabilities. If there are n states in your circular graph, then there would be n^2 states in your torus and so you should expect a n^2 x n^2 transition matrix.

To give any more detail you'll have to specify exactly what you need to know.

James Griffin
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