  In active Brownian motion, an internal propulsion mechanism interacts with
translational and rotational thermal noise and other internal fluctuations to
produce directed motion. We derive the distribution of its extreme fluctuations
and identify its universal properties using large deviation theory. The limits
of slow and fast internal dynamics give rise to a kink-like and parabolic
behavior of the corresponding rate functions, respectively. For dipolar Janus
particles in two and three dimensions interacting with a field, we predict a
novel symmetry akin to, but different from, the one related to entropy
production. Measurements of these extreme fluctuations could thus be used to
infer properties of the underlying, often hidden, network of states.
