  Condensation phenomena are ubiquitous in nature and are found in condensed
matter, disordered systems, networks, finance, etc. In the present work we
investigate one of the best frameworks in which condensation phenomena take
place, namely, the sum of independent and fat-tailed distributed random
variables. For large deviations of the sum, this system undergoes a phase
transition and shifts from a democratic phase to a condensed phase, where a
single variable (the condensate) carries a finite fraction of the sum. This
phenomenon yields the failure of the standard results of the Large Deviation
Theory. In this work we exploit the Density Functional Method to overcome the
limitation of the Large Deviation Theory and characterize the condensation
transition in terms of an order parameter, i.e. the Inverse Participation Ratio
(IPR). This procedure leads us to investigate the system in the large-deviation
regime where both the sum and the IPR are constrained, observing new phase
transitions. As a sample application, the case of condensation phenomena in
financial time-series is briefly discussed.
