Large deviations, condensation and giant response in a statistical system

We study the probability distribution P of the sum of a large number of non-identically distributed random variables n_m . Condensation of fluctuations, the phenomenon whereby one of such variables provides a macroscopic contribution to the global probability, is discussed and interpreted by analogy with phase-transitions in statistical mechanics. A general expression for P is derived, and its sensitivity to the details of the distribution of a single n_m is worked out. These general results are verified by the analytical and numerical solution of some specific examples