On the behaviour of Hodge spectral exponents of plane branches

The Hodge spectral exponents are a discrete set of invariants of an isolated hyper-surface singularity. We study their distribution for the case of plane branches, in terms of numerical invariants of the branch. First, we calculate the limit distribution for different ways of taking the limit. Secondly, we provide a closed formula for the cumulative difference of the distribution of Hodge spectral exponents with a continuous distribution, which is the most common limit. We use this expression to obtain intervals of dominating values.