P04
The statistical mechanics of the interlacement point process
Description
In this project, we will lay the foundations for a new theory of statistical mechanics for point processes of random paths in Euclidean space of unbounded and even infinite lengths. The main novelty will be a proper treatment of the level-three large deviations for the empirical stationary field in large boxes, including a description of the rate function as a new kind of limiting
entropy density. This will make possible a mathematically sound geometric
description of the interacting Bose gas in the condensation regime in the
thermodynamic limit -- this is our main example and the driving force of this
research. We plan to describe the condensate rigorously in terms of an interacting interlacement process. The understanding we expect to obtain
might also be useful in the context of the open problem of finding a proof for
the occurrence of Bose--Einstein condensation.
Preprints/Publications
Alexander Drewitz, Olof Elias, Alexis Prévost, Johan Tykesson, Fredrik Viklund: Percolation for two-dimensional excursion clouds and the discrete Gaussian free field (05/2022)
Orphée Collin, Benedikt Jahnel, Wolfgang König: The free energy of a box-version of the interacting Bose gas (01/2022)
Members
-
Prof. Dr. Alexander Drewitz
Universität zu Köln
Principal Investigator -
Prof. Dr. Benedikt Jahnel
Weierstrass Institute
Principal Investigator -
Prof. Dr. Wolfgang König
Weierstrass Institute
Principal Investigator -
M. Sc. Gioele Gallo
Universität zu Köln
Associated Scientist -
Dr. Karl Olof Hallqvist Elias
Universität zu Köln
Associated Scientist -
Dr. Sanjoy Kumar Jhawar
Weierstrass Institute
Associated Scientist -
Dr. András Tóbiás
Technische Universität Berlin
Associated Scientist -
M. Sc. Ahn Duc Vu
Weierstrass Institute
Associated Scientist -
Dr. Alexander Zass
Weierstrass Institute
Associated Scientist
