Abstract: Condensation is the phenomenon whereby a finite fraction of some quantity, e.g. a particle density, concentrates into a small region of phase-space, as in the paradigmatic example of a vapor transforming into a liquid when crossing a phase-transition. Condensation is observed in a number of different models, related to magnetic properties, gravity, mass transport, bosonic properties etc... In this case condensation is a property of the typical state of the system, that is to say it is observed by monitoring average properties.

A different manifestation of condensation is observed when probability distributions of a fluctuating collective variable, such as the number of particles in a thermodynamic system, are considered. In this case, a fluctuation well above the typical value can be associated to a condensed configuration of the system. This phenomenon, referred to as condensation of fluctuations, was observed for quantities as diverse as particle number, energy, exchanged heats, particles currents etc... This phenomenon is distinct, in principle, from the usual "condensation on average", despite a unified mathematical description is possible in many cases.

In this talk I will discuss the phenomenon of condensation of fluctuations on general grounds by considering some examples taken from paradigmatic models of Statistical Physics.