3 ms·
> 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 cl
by smokel 1y ago
> 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.
- mturmon 1y agoThanks 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.
- atoav 1y agoI 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).
- smokel 1y agoThe 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 https://www.math.uchicago.edu/~lawler/srwbook.pdf