A particle wanders through a medium scattered with obstacles. Sometimes it pushes them aside like a snowplow, and it was thought that this pushing is what eventually stops the motion. But in three-dimensional space, that mechanism doesn't work.

It turns out that stopping arises from rare events: every so often, a particle randomly finds itself in a trap, and all exits close, as if doors slam shut. The probability of such an event at each step is almost independent of how many steps have already been taken. Therefore, the number of particles that haven't gotten stuck decays exponentially, like tea cooling down.

This discovery allows predicting how far a particle will travel in a given time, knowing only two numbers: its typical speed and the probability of getting stuck at one step. Such a simple rule works across different lattices and dimensions.

This view of motion in porous media helps understand how drugs spread through tissues, pollutants through soil, or heat through insulation. Rare but decisive events turn out to be more important than constant friction.