  We study the large deviation function for the empirical measure of diffusing
particles at one fixed position. We find that the large deviation function
exhibits anomalous system size dependence in systems that satisfy the following
conditions: (i) there exists no macroscopic flow, and (ii) their space
dimension is one or two. We investigate this anomaly by using a contraction
principle. We also analyze the relation between this anomaly and the so-called
long-time tail behavior on the basis of phenomenological arguments.
