Phase diagram of gases with long-range interactions – GaLoPee

We are interested in describing the infinite volume behavior of systems of classical particles whose singular, long-range interactions create analytical and probabilistic challenges. From a mathematical perspective, these systems are large probabilistic objects which requires a wide range of tools in probability theory and functional analysis in order to support and enhance the physical intuition. A central question is to interpret their behavior in a statistical physics sense as the temperature varies. We also study them as a family, and examine the roles of dimension, singularity, and long-range. We aim at giving a unified phase portrait, in regard to properties such as rigidity, hyperuniformity or symmetry breaking. We shall combine tools from stochastic geometry with recent analytical developements, while forging new probabilistic techniques like transportation of point processes.