Pushing-Induced Arrest Across Lattices and Dimensions

Tracer-media interactions can give rise to transport phenomena beyond classical models; e.g., obstacle pushing can eliminate percolation. We demonstrate that the existing "snowplow" mechanism proposed to explain this effect fails in 3D. We show that confinement is governed by emergent trapping-rare "door-closing" events that occur with an approximately constant probability per step at low obstacle densities, thus yielding exponential survival. This allows prediction of the time-dependent mean-squared displacement from short-time estimates of the diffusion constant and trapping probability, providing a minimal description of pushing-induced arrest across lattices and dimensions.