Anomalous Diffusion — CTRW Subordination

Continuous Time Random Walk: ⟨x²⟩ ~ t^α, α ≠ 1 from heavy-tailed waiting times

In a CTRW, the walker takes instantaneous steps but waits between steps for a random time τ drawn from a power-law distribution P(τ) ~ τ^(−1−α). When α < 1: subdiffusion — long trapping events slow the walker. When α > 1: approaches normal diffusion. Lévy flights (heavy-tailed steps) give superdiffusion. The subordination technique rewrites CTRW as Brownian motion time-changed by a stable subordinator — connecting fractional calculus to anomalous transport.