Discrete Stochastic Processes
Random Walks: Why Twice as Far Takes 4× as Long
A drunk on a 100 m bridge: why spread grows like √n, and why twice as far takes four times as long.
What to remember
- Spread grows like √n, so reaching distance d takes about d² steps.
- Fair gambler’s ruin: P(hit N) = k/N and E[T] = k(N − k).
- Volatility scales with √time, which is where √252 comes from.
Read the lessonRandom Walks, with a checkpoint at the end.