Thanks a bunch, looking forward to reading the paper. I am especially intrigued by the claim one can give stronger guarantees than say a simple random walk.
if next_value > upper_bound: next_value = upper_bound
if next_value < lower_bound: next_value = lower_bound
This works fine, but serves to concentrate probability mass near the boundaries, so it's no longer uniformly distributed. By reflecting across boundaries rather than coercing, you're effectively flattening that concentration. If you coerce, you also reduce the expected value, which may or may not be a desirable property.