An example of mathematical authorship attribution

In this paper we discuss a novel mathematical approach to authorship attribution which we implemented recently to face a concrete problem of author recognition. The fundamental ideas for our methods came from Statistical Mechanics and Information Theory. We combine two approaches. Both of them use similarity measures between couples of texts as indicators of stylistic closeness: the first one is based on the comparison of frequencies of fixed length substrings ({it $n$-grams}) throughout the texts; the second one relies on a suitable use of compression algorithms as relative entropy approximators, in the spirit of the so-called Ziv-Merhav's Theorem. The two methods were separately developed and then combined, together with a suitable and theoretically founded ranking analysis, to produce an original authorship attribution procedure that yielded very successful results on the specific problem to which it was applied. This ranking analysis could be of interest also in other application fields.