Shepherd physics: Capturing a skittish lamb, using statistical physics

A trio of theoretical physicists have recently used ideas from statistical mechanics and probability theory to try to develop an optimal strategy for capturing a skittish lamb near a precipice.

The situation that they model is an idealization of “the capture of a diffusing, but skittish lamb, with an approaching shepherd on the left and a precipice on the right.” They approached this problem by examining first-passage probabilities, which describe the first time of some event (e.g., a lamb falling off of a cliff) occurring. The physicists summarized their strategy as follows:

In particular, the probability to capture the lamb is maximized when the shepherd moves at a non-zero optimal speed if the initial lamb position and the ratio between the two boundary speeds satisfy certain conditions.

Here’s further detail from the study:


One of the physicists, Sid Redner, works at the Santa Fe Institute, so perhaps the next problem he’ll attempt is to design a strategy to help Wile E. Coyote catch the Roadrunner.

BONUS: Redner on the question: In a pro basketball game, when is a lead safe?