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Comment by smokel | Hacker News Reader

> There is one chance in ten that the walker will take a positive or negative step along any given dimension at each time point.

This confused me a bit. To clarify: at each step, the random walker selects a dimension (with probability 1/10 for any given dimension), and then chooses a direction along that dimension (positive or negative, each with probability 1/2). There are 20 possible moves to choose from at any step.

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Thanks for this. It goes back to the node connectivity graphs he shows just above that statement.

He is thinking about a random choice among the 20 edges branching out from each vertex.

I thought multidimensional random walkers would make random choices on all dimensions, so:

  step = [random.choice([-1,0,1]) for _d in range(n_dimensions)]

At least this is how I did 2D random walks as this allows for diagonal steps (with the downside that the walker travels longer steps in that direction).

The common definition for random walks moves only by unit vectors. Unfortunately, the information on Wikipedia is somewhat limited. The book "Random Walk: A Modern Introduction" (2010) by Gregory Lawler describes things in the first chapter, and is available online for free [1].

[1] https://www.math.uchicago.edu/~lawler/srwbook.pdf

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