Considerable efforts have been devoted to the study of non-Gaussian fluctuations such as Lévy statistics, generalizing the standard description of random walks. Often, only macroscopic signatures, obtained by averaging over many random steps, are observed in physical systems. I will present experimental results investigating the elementary process of anomalous diffusion of photons in hot atomic vapours. We measured the step-size distribution of the random walk and show that it follows a power-law characteristic of Lévy flights . We also show how single shot images can allow to extract the Lévy exponent in hot atomic vapours, which correspond to systems with annealed disorder .
 Lévy Flights of Photons in Hot Atomic Vapors, N. Mercadier, W. Guerin, M. Chevrollier and R. Kaiser, Nature Physics 5, 602 - 605 (2009).
 Signatures of Lévy flights with annealed disorder, Q. Baudouin, R. Pierrat, A. Eloy, E.J. Nunes-Pereira, P.-A. Cuniasse, N. Mercadier, and R. Kaiser, Phys. Rev. E 90, 052114 (2014)