Founding a mathematical diffusion model in linguistics. The case study of German syntactic features in the North-Eastern Italian dialects
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We take as a case study the spread of Germanic syntactic features into Romance dialects of North-Eastern Italy, which occurred after the immigration of German people in the Tyrol during the High Middle Ages. An interactive map is produced using tools of what is called Geographic Data Science. A smooth two-dimensional surface 𝒢 expresses locally which fraction of territory uses a given German language feature: it is obtained by interpolating a discrete function that says if at any surveyed locality that feature is used or not.This surface 𝒢 is thought of as the value at the present time of a function describing a diffusion-convection phenomenon in two dimensions (here said tidal mode), which is subjected in a very natural way to the same equation, suitably contextualized, used in physics for a number of phenomenological facts like the heat diffusion. It is shown that solutions of this equation, evaluated at the present time, fit well with the data as interpolated by 𝒢, thus providing convincing pictures of diffusion-convection of the linguistic features of the case study, albeit simplifications and approximations.Very importantly, it is shown that Schmidt's 'waves' can be counted among the solutions of the diffusion equation: superimposing Schmidt 'waves' to a 'tidal flooding' can reproduce complexities of real linguistic diffusion events.
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