In this paper, we study spectral measures whose square integrable spaces admit a family of exponential functions as an orthonormal basis. First, we characterize the spectrality of infinite convolutions generated by a sequence of admissible pairs. Next, we show that given finitely many admissible pairs, almost all random convolutions are spectral measures. Moreover, we give a complete characterization of spectrality of random convolutions for some special cases.
Comment: 29 pages