P13
Renormalization group for Gibbs point processes
Description
Proving the existence of phase transitions and condensation for particles in continuous space is a challenging open problem in mathematical statistical
physics. We propose a program to make the droplet picture of condensation
rigorous. The key tool to be developed is a renormalization group theory for
Gibbs point processes that is applied to mixtures of droplets, for example
mixtures of hard spheres of different sizes. The relevant systems are multiscale; different scales correspond to different droplet sizes. In the new renormalization theory, the superposition principle of Poisson point processes
plays a role similar to the additivity of covariances of independent Gaussian
fields. We apply the theory to compute free energies and density functionals
and to prove first-order phase transitions. The program is of direct relevance
to Gibbs hard-core models in stochastic geometry and connects to diagrammatic techniques for point processes. The droplet picture is also highly
relevant for effective coagulation-fragmentation models in dynamic studies
of condensation and metastability.
Preprints/Publications
No preprints from this project yet.Members
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Prof. Dr. Sabine Jansen
Ludwig-Maximilians-Universität München
Principal Investigator -
M. Sc. Leonid Kolesnikov
Ludwig-Maximilians-Universität München
Associated Scientist -
M. Sc. Jan Philipp Neumann
Ludwig-Maximilians-Universität München
Associated Scientist -
M. Sc. Stefan Wagner
Ludwig-Maximilians-Universität München
Associated Scientist