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There exist important stochastic physical processes involving infinite meanwaiting times. The mean divergence has dramatic consequences on the processdynamics. Fractal time random walks, a diffusion process, and subrecoil lasercooling, a concentration process, are two such processes that lookqualitatively dissimilar. Yet, a unifying treatment of these two processes,which is the topic of this pedagogic paper, can be developed by combiningrenewal theory with the generalized central limit theorem. This approachenables to derive without technical difficulties the key physical propertiesand it emphasizes the role of the behaviour of sums with infinite means.Comment: 9 pages, 7 figures, to appear in the Proceedings of Cargese Summer  School on "Chaotic dynamics and transport in classical and quantum systems

Fractal Time Random Walk and Subrecoil Laser Cooling Considered as Renewal Processes with Infinite Mean Waiting Times