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In this paper we present a low-temperature (T < 30 K) photoluminescence (PL) study of space-indirect excitons in GaAs/AlGaAs double quantum wells at pumping density P and external electric field V dc . At certain external parameter values (P , T and V dc ) part of the spectral profile of the indirect exciton (IX) line reveals an enormous increase (shot) of PL intensity (threefold), which fluctuates in time on the characteristic scale of tens of seconds. To explain this anomalous behaviour we use the theoretical model of the Bose-Einstein condensation effect which takes place in a system of 2D bosons which, in addition to extended states, have a discrete energy spectrum below the bottom of the free zone.