Nonlinear distributional fixed-point equations in statistical mechanics

• Applicant: Professor Dr. Sebastian Mentemeier
• Subject Area: Mathematics
• Term: from 2017 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 392119783

In numerous stochastic models, the probability distribution of quantities of interest can only be described implicitly, as solutions of so-called distributional fixed-point equations. While linear distributional fixed-point equations have been studied intensively there is no theory of nonlinear distributional fixed-point equations, although such equations appear prominently in active fields of research in statistical physics.The aim of my project is to study nonlinear distributional fixed-point equations, starting from concrete examples. Relevant questions concern the existence and uniqueness of solutions and their properties, such as smoothness or tail behaviour.These results will help to simplify calculating critical parameters in spin models and will provide new insights into equilibrium distributions of ideal gases.

• DFG Programme: Research Grants