Abstract
In recent years Italy has been involved in massive migration flows and, consequently, migrant integration is becoming a urgent political, economic and social issue. In this paper we apply quantitative methods, based on probability theory and statistical mechanics, to study the relative integration of migrants in Italy. In particular, we focus on the probability distribution of a classical quantifier that social scientists use to measure migrant integration, that is, the fraction of mixed (natives and immigrants) married couples, and we study, in particular, how it changes with respect to the migrant density. The analysed dataset collected yearly by ISTAT (Italian National Institute of Statistics), from 2002 to 2010, provides information on marriages and population compositions for all Italian municipalities. Our findings show that there are strong differences according to the size of the municipality. In fact, in large cities the occurrence of mixed marriages grows, on average, linearly with respect to the migrant density and its fluctuations are always Gaussian; conversely, in small cities, growth follows a square-root law and the fluctuations, which have a much larger scale, approach an exponential quartic distribution at very small densities. Following a quantitative approach, whose origins trace back to the probability theory of interacting systems, we argue that the difference depends on how connected the social tissue is in the two cases: large cities present a highly fragmented social network made of very small isolated components while villages behave as percolated systems with a rich tie structure where isolation is rare or completely absent. Our findings are potentially useful for policy makers; for instance, the incentives towards a smooth integration of migrants or the size of nativist movements should be predicted based on the size of the targeted population.
Highlights
Systems made of a large number of components can be suitably analysed with probability theory and statistical mechanics formalism
By further analyzing the quantifier probability distribution around the critical point, we find that large municipalities display Gaussian fluctuations while small municipalities fluctuate according to a quartic exponential distribution close to γc
Our interpretation is based on a series of rigorous mathematical works (Alberici et al, 2014a, b; Alberici and Contucci, 2014; Alberici et al, 2015, 2016a, b) where it has been shown that, in the presence of an imitative interaction among vertices, the model displays a phase transition: the dimer densities have a square-root growth by the critical point, where quartic exponential fluctuations are observed at the scale N3/4
Summary
Systems made of a large number of components can be suitably analysed with probability theory and statistical mechanics formalism. Since this feature is generally the signature of a mixture of two, or more, different phenomena that need to be disentangled we split the database into large and small municipalities with respect to a proper tuning of a threshold θ over the population size.
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