Measurements of the electronic current fluctuations of free-standing hydrogenated amorphous silicon nanoparticles are described. The nanoparticles are synthesized by high-density plasma chemical vapor deposition and are deposited onto conducting substrates. An insulating matrix, either silicon oxide or silicon nitride is then grown in order to electrically isolate the particles. Electronic measurements are performed in this transverse geometry, and underneath a top electrode of area 1mm x 1mm are typically 10,000 nanoparticles with an average diameter of 150 nm in parallel. The spectral density of the current fluctuations in the a-Si:H nanoparticles is well described by a 1/f frequency dependence for frequency f, as in the case of bulk a-Si:H films. The variation of the correlation coefficients with frequency octave separation of the noise power fluctuations in bulk a-Si:H films indicates serial interactions between fluctuators. In contrast, the octave separation dependence of the correlation coefficients for the nanoparticles are very well described by an ensemble of fluctuators whose amplitudes are independently modulated in parallel.