Why The Book Has A Power-Law Shape

If you plot the average quantity of resting orders at each price level away from the best bid or ask, you don't get a bell curve or a flat shelf — you get a shape that looks roughly like $1/d^\alpha$, where $d$ is distance in ticks from the best quote and $\alpha$ is typically between 0.5 and 1.5 depending on the stock and venue. That means depth is thin and fragile right at the touch, builds up as you move a few ticks away, and then decays slowly — a "fat tail" of resting liquidity that never really disappears, unlike an exponential decay which would vanish quickly.

This shape matters because it explains two things traders see constantly: why a market order can walk through several price levels with surprisingly little resistance right near the best price (the top of book is thin), and why very large orders eventually find enough resting size to fill if they're willing to walk far enough into the book (the tail is fat, not empty). A purely exponential or normal-shaped book would predict a hard wall a few ticks out; a power-law book predicts liquidity that keeps thinning gradually, without a clean cutoff.

Worked illustration: if depth at distance $d$ ticks scales as $q(d) \propto d^{-1}$, then depth at 10 ticks out is roughly 10 times thinner than at 1 tick, and depth at 100 ticks is roughly 100 times thinner than at 1 tick — but never literally zero, which is why market impact models for large orders use a power-law (or square-root) impact function rather than assuming a fixed depth "wall."