  We study local features, and provide a topological insight into the global
structure of the probability density distribution and of the pattern of the
optimal paths for large rare fluctuations away from a stable state. In contrast
to extremal paths in quantum mechanics, the optimal paths do {\it not}
encounter caustics. We show how this occurs, and what, instead of caustics, are
the experimentally observable singularities of the pattern. We reveal the
possibility for a caustic and a switching line to start at a saddle point, and
discuss the consequences.
