Dependent continuum percolation
A talk in the Kolloquium Mathematische Physik series by
Markus Heydenreich from Uni Augsburg
| Abstract: |
We introduce the weight-dependent random connection model as a
prototypic model for complex networks: vertices are given as a marked
Poisson processes and edges are inserted with a probability depending on
the spatial distance and the marks of the two endpoints.
The vertex marks introduce a specific dependence structure that make the
model very versatile, and it generalises various complex network models
in the literature.
In the first part of the talk, I will motivate the model and discuss
structural results of the connected components.
The second part concerns the percolation phase transition: Upon
variation of the Poisson density, a percolation phase transition occurs
under mild conditions: for low density there are finite connected
components only, while for large density there is an infinite component
almost surely.
We establish the existence of various mean-field critical exponents,
that characterise the phase transition the low- and high-density phase,
in high-dimensional Euclidean space.
Based on joint works with Alejandro Caicedo, Matthew Dickson, Peter
Gracar, Christian Mönch, Peter Mörters.
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