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Abstract: We study statistical relationships between bubble walls in cosmological first-order phase transitions. We consider the conditional and joint probabilities for different points on the walls to remain uncollided at given times. We use these results to discuss surface correlations which are relevant for the consequences of the transition. In our statistical treatment, the kinematics of bubble nucleation and growth is characterized by the nucleation rate and the wall velocity as functions of time, and we obtain general expressions in terms of these two quantities. As a specific example, we consider a model with simultaneous nucleation and constant velocity.