Quantum Random Walks Archive

This is a link to the 200-step animation of the 1-D Hadamard QRW, courtesy of Joe Chang; it is shown next to a 1-D classical random walk.

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Some questions generated by the pictures:

When there are multiple peaks, are these always due to folds in the Gauss map (the logarithmic gradient map from {H=0} intersect the two-torus to RP^1)?

When a peak does not appear infinite, is this due to the numerator vanishing there, or is it actually infinite even though appearing small at scale 200?

Do the very large individual points always correspond to a factor (1 + y x^k) in the denominator? If so, how can you tell when such a factor will arise -- what does this say about the matrix and is such an occurrence non-generic?

Look at 4-chirality walks #2 and #6. These appear to have a huge peak but not to factor -- someone explore these!

One Dimensional, 3 chirality walks
One Dimensional, 4 chirality walks
Two Dimensional, 4 chirality walks
Three Dimensional, 6 chirality walks