Probabilistic Graph Theory
This area represents one of the most active frontiers in modern probability theory, with applications ranging from studying social networks to developing sophisticated algorithms for probabilistic machine learning and neural networks.
The research group focuses on investigating interacting particle systems and various random discrete structures and algorithms. Recent developments in this field include introducing new Markov structures on fully connected graphs, exploring competing Branching Random Walks on integer lattices, studying the frog model, and analyzing water transport on finite graphs.
This research extends into spatial interacting particle systems and statistical physics, emphasizing discrete probability theory. These studies are deeply connected to models in physics, opinion formation processes, and the dynamics of disease spreading. The research contributes significantly to our ability to forecast and understand complex real-world phenomena, improving our grasp of various interaction models.