Subdiffusive CTRW — Lévy Subordination
Continuous-time random walk with heavy-tailed waiting times, ⟨x²⟩ ~ t^α
Subdiffusion arises in a CTRW when waiting times τ follow a Lévy-stable distribution with tail P(τ>t) ~ t^{−α}, 0<α<1 — trapping events with no finite mean. Via Lévy subordination, the process is a Brownian motion B(s) evaluated at a random operational time S(t), where S follows an α-stable subordinator. The MSD ⟨x²(t)⟩ ~ t^α instead of t, reflecting anomalous diffusion in disordered media, crowded cells, and glasses.