<p>The dynamic responses of a railway bridge subject to a moving train are randomly affected by track irregularities. With particular attention on track random irregularities, an in-depth analysis is performed in this study to achieve the uncertainty quantification of train-track-bridge interactions. In the method, a 3D train-bridge dynamic model is constructed, in which the ballastless tracks and the bridge girders are integrated as an integral system, and the nonlinear wheel-rail interactions are considered. The track-bridge time-varying coupled method is introduced to improve the modeling and solution efficiency. As the main system excitation, a method for characterizing the ergodic wavelength and amplitude properties of track irregularities is introduced, through which the train-track-bridge system responses can be fully revealed. By introducing a probability density evolution method, an accurate and efficient probabilistic assessment of the influence of track random irregularities on system responses can be achieved. In comparison with the generally used methods, this present work is capable of conducting more complete and accurate evaluation for random vibrations of train-track-bridge systems. Furthermore, the stability of train operation and ride comfort are evaluated for different running speeds and different track geometric conditions. The results show that considering the impact of full probability irregularities is crucial in the random analysis of the train-track-bridge system.</p>