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Experimental studies are presented of the random fluctuations of the laser light and of the diode current of continuous-wave multifilament GaAs laser diodes. Using the single-detector method, the intensity noise of the laser light of single, optically isolated filaments is measured in the central measuring frequency range 40 kHz-6 MHz. In the same frequency range, the intensity noise of the total laser light from one emitting face is also measured. The intensity noise of the laser light is found to depend strongly on the generation of lasing filaments in the p-n junction. The noise of the electrical excitation current depends also on the filamentary action. The laser-light noise and the current noise are correlated. The cross-correlation coefficient is measured between 40 kHz and 6 MHz as a function of the excitation current. The discovered correlation allows the application of a noise-modulation method to the laser light, which leads to a reduction of the laser-light noise-to-signal ratio.