Image blurring as a result of stochastic particle–particle interactions has been investigated for projection electron‐ and ion‐beam lithography systems. A comparative analysis of the currently available analytical theories is presented. The results from these theories are also compared with Monte Carlo simulation results and experimental data. Large variations in results and serious disagreements between the different theoretical approaches are found. We have formulated a new theory on the basis of a simple, analytical approach that overcomes most of the difficulties experienced by earlier theories with two key concepts: consideration of nearest‐neighbor interactions only, and a randomization length, over which the interactions are correlated. Our model displays satisfactory functional and numerical agreement with Monte Carlo simulation results over a large range of beam currents, as well as with the only available experimental data. The physical basis of our model also enables us to understand the origins of the discrepancies arising from earlier theories. ©1995 American Institute of Physics.