Optimal graphs, local perturbations and fixation for interacting particle systems and complexity

Research Project, 2026 – 2030

The research project consists of four subprojects. The first two subprojects concerninteracting particle systems (IPS). In the first subproject, the number of agents is finite, and the goal is to determine which of the possible IPS parameters maximizes some natural quantitysuch as the absorption time. Another goal in this subproject is to determine which limiting distributions can ariseas the size of the system grows when one considers for example the absorption time.In the second subproject, the goal is to understand which infinite interacting particle systems fixate, meaningthey converge to an absorbing state. The goal of the third subproject, which is in the field of theoretical computer science, is to understandthe relationship between different notions of "distributional complexity" for Boolean functions.The fourth subproject concerns monotonicity of payoffs in dart problems as a function of the distance tothe target and the goal is to determine how this depends on the dart distribution.We think that within the time frame of this project, one will be able to obtain a number of results. There is no real "project organization" and the methods can be somewhat adhoc. However, for the second subproject, we plan to use techniques from ergodic theory, such as entropy theory.We believe the planned research is important since, if successful, it will shed light on a number ofnatural and foundational problems in probability theory and also in theoretical computer science.