Dr Peter Gracar

Responsibilities

• Early Career Champion

Research interests

Multi-scale percolation

When studying interacting particle systems, it is often useful to describe their behaviour in bounded regions and then draw conclusions from that. Paired with time intervals this allows us to tessellate space-time into cells on which the occurence of events of interest within a cell can be seen as a dependent percolation problem. Classical percolation tools fail due to the infinite range dependence in this space-time percolation problem, so the problem has to be considered at increasingly large scales to capture sufficiently much information.

Inhomogeneous random graphs

If one interprets nodes as individuals and edges as them having a relationship, then inhomogeneous random connection models yield a rich class of models that can describe phenomena such as people with similar interests being more likely to form bonds or the famous 6 degrees of separation problem. Mathematically, these effects can be studied with inhomogeneous random graphs and then analyzing typical distances or the existence of certain kinds of paths within the graph.

Research groups and institutes

• Probability and Financial Mathematics
• Statistics

Projects

<li><a href="//phd.leeds.ac.uk/project/1889-mobile-geometric-scale-free-random-graphs">Mobile Geometric Scale-Free Random Graphs</a></li>