“Scale-free percolation in continuous space”
Venerdì 5 Febbraio 2021, ore 14:30 - Zoom - Michele Salvi (Università di Roma Tor Vergata)
The scale-free percolation random graph features three fundamental properties that are often present in large real-world structures (social networks, communication networks, inter-banking systems and so on), but which are never present at once in classical models: (1) Scale-free: the degree of the nodes follows a power law; (2) Small-world: two nodes are typically at a very small graph distance; (3) Positive clustering coefficient: two nodes with a common neighbour have a good chance to be linked. We study a continuous version of scale-free percolation and its possible application to the statistical analysis of a dataset provided by the French Ministry of Agriculture. We discuss some stochastic processes (random walks and particle systems) on these kinds of structures with the final goal of understanding how an epidemic would spread.