> Markets are random walks so they exhibit a fairly fixed distribution of different sized crashes.

Market prices being unpredictable random walks doesn't mean that the volatility or shape needs to be constant. To make the notation more precise, you need to talk about (sub-) martingales.

> If they deviated, someone could notice that pattern and trade on it, returning the market back to a random walk.

This is true, but "fairly fixed distribution of different sized crashes." doesn't follow at all.