From Parisi to Boltzmann, II. Via TAP and GREM.

• Applicant: Professor Dr. Ralph Neininger, since 5/2024
• Subject Area: Mathematics
• Term: since 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 432176920

This research proposal is the continuation of my project "From Parisi to Boltzmann". The new goals have thus cogently emerged from our research activities in the past 3 years. In particular, we have identified the hitherto missing link between Derrida's GREM(s) and the TAP free energy. The REM-TAP approximation has already been worked out, so here the next (natural) steps: we will do a similar analysis but with the help of GREM-structures, more precisely: calculate the free energy in the infinite volume limit, then tackle the Gibbs measure and then the macroscopic cavity dynamics. All of these intermediate steps are necessary to achieve the "ultimate" goal: the Parisi fixed point equation. A second research project that has emerged from our TAP-studies concerns a Stein-approach to the true TAP equations, i.e. with with classical Onsager correction (and not its P-almost sure limit, as done in the literature so far). A third goal of this extension is the preparation of a separate research proposal concerning the Babylonian formulas for spin systems which I have recently derived.

• DFG Programme: Research Grants
• International Connection: USA
• Cooperation Partner: Professor Louis-Pierre Arguin
• Co-Investigators: Professor Dr. Christian Brennecke; Dr. Adrien Schertzer; Dr. Marius Alexander Schmidt
• Ehemaliger Antragsteller: Professor Dr. Nicola Kistler, until 5/2024