Scale-free percolation on finite domains

• Applicant: Professor Dr. Markus Heydenreich
• Subject Area: Mathematics
• Term: from 2017 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 386248531

The proposal considers a mathematical model for a random network that features many properties observed in real-world networks: (i) it is scale free, i.e. vertices have power law degree; (ii) it is spatial, i.e. connectivity is determined by the position of the vertices in Euclidean space; 
(iii) it is small world, i.e. connections in the network are small w.r.t. distance in the Euclidean space. A prime example of such a model is scale-free percolation, which is a model on the infinite lattice. This proposal concerns such models on finite domains, such as the boxes, tori or hypercubes. Establishing structural properties of these models and studying asymptotics as the network size increases is a challenging task for the project. The role of boundary conditions is investigated as well as phase transitions. We finally address the question of navigation through the resulting random network. This is a project in probability theory. The topic has connections with discrete mathematics (in particular random graph theory) and statistical mechanics.

• DFG Programme: Research Grants