If the question is "does causation imply linear correlation", then the answer is obviously and trivially "no". But we don't need a PRNG to see that. Take a ser

If the question is "does causation imply linear correlation", then the answer is obviously and trivially "no". But we don't need a PRNG to see that. Take a series of chutes whose entrances are lined up in a row, and whose exits are arranged in a circle. Now start dropping balls in the entrances and see where they end up. Obviously there is a causal relationship between where we drop the ball and where it lands, but it's not a linear correlation. But there's still a correlation.