Refined data analysis for local marriages in Italy.

Panel a: log-log scale plot of LMαi,y versus Γαi,y, where different regions are denoted in different colours and symbols, as explained in the legend. As discussed in the text, these data are particularly noisy, yet one can bin the whole set of data (green squares) and get the best-fit (solid line). This is given by the function , in agreement with the theoretical result (2). The best-fit coefficients are a = 1.96 and b = −1.59 ⋅ 10−4. Notice that the parameter b accounts for the standard deviation associated to binned data. It is clear, even by visual inspection, that most regions systematically deviate from the best-fit curve. In the insets we show, as examples, the data pertaining to two selected regions, namely Emilia-Romagna (upper inset) and Campania (lower inset). Notice that the related data lay, respectively, below and above the best-fit curve previously obtained for the whole data set (solid line). Panel b: For each region we calculate ρα, as defined in the text and deepened in the Theoretical Protocol Section. The horizontal line is drawn as a reference for the unitary value. Notice that, for most regions, the deviation with respect the unitary value is significant. From this plot we can distinguish regions displaying a relatively large number of marriages (i.e., ρα > 1) and regions displaying a relatively small number of marriages (i.e., ρα c. Remarkably, regions exhibiting analogous deviations share a sharp geographical proximity: regions with ρα > 1 (bright shading) correspond to Southern Italy, while regions with ρα d: the two clusters of regions highlighted are analysed separately. For each we bin the related raw data and get a best fit, still according to the function , obtaining aup = 2.29 and bup = −4.39 ⋅ 10−4 (R2 = 0.98) for the set of regions with ρα > 1, and adown = 1.66 and bdown = −1.52 ⋅ 10−4 (R2 = 0.99) for the set of regions with ρα aup/adown ≈ 1.4. Binned data for the former set (triangles) and for the latter set (square) are shown in the main panel, together with the related best fits, in a log-log scale plot. These fits are significantly better that the one obtained at the country level, suggesting the existence of internal heterogeneities. In the insets we compare these best fits with raw data for two regions (Calabria and Campania) with ρα > 1 (upper inset) and two regions (Emilia-Romagna and Lombardy) with ρα