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.
Large deviations, condensation and giant response in a statistical system
CORBERI, Federico
2015-01-01
Abstract
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.File in questo prodotto:
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