Abstract
Hodge spectral exponents are a discrete set of invariants of an isolated hypersurface singularity. In this work, we study their distribution for the case of irreducible plane curves, in terms of numerical invariants of the curve. First, we obtain a necessary condition for the limit distribution to be a continuous distribution, which is the most common limit. Second, we give a closed formula for the cumulative difference between the distribution of Hodge spectral exponents and the continuous distribution, and we obtain intervals of dominant values. Finally, we characterize the families of irreducible plane curves for which the limit distribution is the continuous distribution.