Lévy flights of photons with infinite mean free path

Multiple scattering of light by resonant vapor is characterized L\'evy-type superdiffusion with a single-step size distribution $p(x)\ensuremath{\propto}1/{x}^{1+\ensuremath{\alpha}}$. We investigate L\'evy flight in hot rubidium collisional-broadened 50 torr He gas. The frequent collisions produce Lorentzian absorptive and emissive profiles $\ensuremath{\alpha}<1$ corresponding divergent mean step size. extract the parameter $\ensuremath{\alpha}\ensuremath{\approx}0.5$ multiple-scattering regime from radial profile transmission violation Ohm's law. measured total diffusive curves are well reproduced numerical simulations for line shapes.