We present theoretical and experimental results of Levy 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 Levy-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 Ohms law [T_(diff) proportional to L^(-alpha/2) different from 1/L], as expected for a Levy 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 Levy parameter alpha under macroscopic multiple scattering conditions paving the way to investigation of Levy flights in different atomic physics and astrophysics systems.
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