Stochastic processes on evolving networks

• Applicant: Privatdozent Dr. Anton Klymovskiy
• Subject Area: Mathematics
• Term: from 2019 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 412848929

In the last 20 years, complex networks became a key tool to model real-world complex systems in the sciences. Yet, the majority of networks evolve over time and this can have a substantial effect on the processes unfolding on them. Moreover, the influence can also go the other way around: processes happening on a network can affect the evolution of the network itself leading to what is called coevolution in adaptive networks (or more generally in complex adaptive systems). Examples include epidemiological and ecological networks, neural networks, systems biology networks, social networks, financial markets, etc. In all these contexts, there is a great deal of uncertainty/volatility in the structure and dynamics of the complex system.What are the emerging global patterns in complex systems? How do they come about from the behavior of the elements? These are typical questions in the sciences, economy and policy making. These questions immediately lead to severe mathematical problems about the models of complex systems but also about their relationships with the real data.It is the purpose of this scientific network to advance the rigorous mathematical theory of stochastic processes on (co)evolving networks. The scientific network focuses on:(a) The probabilistic underpinnings of stochastic processes on (co)evolving networks.(b) Analysis and synthesis of key examples coming from the areas of information/opinion exchange processes, population dynamics, infection processes, and dynamics of artificial neural networks.(c) Issues of statistical inference, estimation and uncertainty quantification for (evolving) complex networks and processes on them.

• DFG Programme: Scientific Networks