  We present theoretical and experimental results of L\'evy flights of light
originating from a random walk of photons in a hot atomic vapor. In contrast to
systems with quenched disorder, this system does not present any correlations
between the position and the step length of the random walk. In an analytical
model based on microscopic first principles including Doppler broadening we
find anomalous L\'evy-type superdiffusion corresponding to a single-step size
distribution P(x) proportional to x^(-1-alpha), with alpha=1. We show that this
step size distribution leads to a violation of Ohm's law [T_(diff) proportional
to L^(-alpha/2) different from 1/L], as expected for a L\'evy walk of
independent steps. Furthermore the spatial profile of the transmitted light
develops power law tails [I(r) proportional to r^(-3-alpha)]. In an experiment
using a slab geometry with hot rubidium vapor, we measured the total diffuse
transmission T_(diff) and the spatial profile of the transmitted light
T_{diff}(r). We obtained the microscopic L\'evy parameter alpha under
macroscopic multiple scattering conditions paving the way to investigation of
L\'evy flights in different atomic physics and astrophysics systems.
