Large deviations, condensation, and giant response in a statistical system

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 in analogy to 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.

New improved and extended version (12 pages, 4 figures) with more references and additional discussions. To appear in J. Phys. A: Math. Theor

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Cited by in corpus (14)

• Large fluctuations and dynamic phase transition in a system of self-propelled particles
• Anomalous scaling of dynamical large deviations
• Localization transition in the Discrete Non-Linear Schrödinger Equation: ensembles inequivalence and negative temperatures
• Condensation transition in large deviations of self-similar Gaussian processes with stochastic resetting
• Heat fluctuations of Brownian oscillators in nonstationary processes: fluctuation theorem and condensation transition
• Work fluctuations of self-propelled particles in the phase separated state
• Condensation for random variables conditioned by the value of their sum
• Development and regression of a large fluctuation
• Probability distributions with singularities
• Anomalous scalings of fluctuations of the area swept by a Brownian particle trapped in a $|x|$ potential
• Condensation of degrees emerging through a first-order phase transition in classical random graphs
• Dynamics of fluctuations in the Gaussian model with conserved dynamics
• Subleading-order theory for condensation transitions in large deviations of sums of independent and identically distributed random variables
• Dynamics of fluctuations in the Gaussian model with dissipative Langevin Dynamics