The statistical mechanics of the interlacement point process


Description Phase 1

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

Wolfgang König, Quirin Vogel, Alexander Zass: Off-diagonal long-range order for the free Bose gas via the Feynman--Kac formula (12/2023)

Benedikt Jahnel, Christof Külske, Alexander Zass: Locality properties for discrete and continuum Widom--Rowlinson models in random environments (11/2023)

Benedikt Jahnel, Jonas Köppl, Bas Lodewijks, András Tóbiás: Percolation in lattice k-neighbor graphs (06/2023)

Myriam Fradon, Julian Kern, Sylvie Roelly, Alexander Zass: Diffusion dynamics for an infinite system of two-type spheres and the associated depletion effect (06/2023) published

Benedikt Jahnel, Jonas Köppl: On the long-time behaviour of reversible interacting particle systems in one and two dimensions (03/2023)

Benedikt Jahnel, Lukas Lüchtrath: Existence of subcritical percolation phases for generalised weight-dependent random connection models (02/2023)

Benedikt Jahnel, Jonas Köppl: Trajectorial dissipation of Φ-entropies for interacting particle systems (01/2023) published

Elie Cali, Alexander Hinsen, Benedikt Jahnel, Jean-Philippe Wary: Chase-escape in dynamic device-to-device networks (11/2022) published

Elie Cali, Alexander Hinsen, Benedikt Jahnel, Jean-Philippe Wary: Connectivity in mobile device-to-device networks in urban environments (08/2022) published

Benedikt Jahnel, Sanjoy Kumar Jhawar, Anh Duc Vu: Continuum Percolation in a Nonstabilizing Environment (05/2022) published

Alexander Drewitz, Olof Elias, Alexis Prévost, Johan Tykesson, Fredrik Viklund: Percolation for two-dimensional excursion clouds and the discrete Gaussian free field (05/2022)

Benedikt Jahnel, Jonas Köppl: Dynamical Gibbs Variational Principles for Irreversible Interacting Particle Systems with Applications to Attractor Properties (05/2022) published

Christian Hirsch, Benedikt Jahnel, Stephen Muirhead: Sharp phase transition for Cox percolation (03/2022) published

Orphée Collin, Benedikt Jahnel, Wolfgang König: A micro-macro variational formula for the free energy of a many-body system with unbounded marks (01/2022) published

Nils Engler, Benedikt Jahnel, Christof Kuelske: Gibbsianness of locally thinned random fields (01/2022) published

Christian Hirsch, Benedikt Jahnel, Elie Cali: Connection intervals in multi-scale dynamic networks (11/2021) published

Martin Heida, Benedikt Jahnel, Anh Duc Vu: Stochastic Homogenization on Irregularly Perforated Domains (10/2021)

Benedikt Jahnel, Christof Kuelske: Gibbsianness and non-Gibbsianness for Bernoulli lattice fields under removal of isolated sites (09/2021) published

Cristian F. Coletti, Lucas R. de Lima, Alexander Hinsen, Benedikt Jahnel, Daniel Valesin: Limiting shape for First-Passage Percolation models on Random Geometric Graphs (09/2021) published

Christian Hirsch, Benedikt Jahnel, Elie Cali: Percolation and connection times in multi-scale dynamic networks (03/2021) published

Benedikt Jahnel, András Tóbiás: Absence of percolation in graphs based on stationary point processes with degrees bounded by two (10/2020) published

Benedikt Jahnel, András Tóbiás, Elie Cali: Phase transitions for the Boolean model of continuum percolation for Cox point processes (03/2020) published

Benedikt Jahnel, András Tóbiás: SINR percolation for Cox point processes with random powers (12/2019) published

Alexander Hinsen, Benedikt Jahnel, Elie Cali, Jean-Philippe Wary: Phase transitions for chase-escape models on Gilbert graphs (11/2019) published

Christian Hirsch, Benedikt Jahnel, András Tóbiás: Lower large deviations for geometric functionals (10/2019) published

András Tóbiás, Benedikt Jahnel: Exponential moments for planar tessellations (02/2019) published

Codina Cotar, Benedikt Jahnel, Christof Külske: Extremal decomposition for random Gibbs measures: From general metastates to metastates on extremal random Gibbs measures (10/2018) published

Benedikt Jahnel, Wolfgang König: Probabilistic methods for telecommunications (06/2018) published

Golibjon Botirov, Benedikt Jahnel: Phase transitions for a model with uncountable spin space on the Cayley tree: the general case (03/2018) published

Members

  • member's portrait

    Prof. Dr. Alexander Drewitz

    Universität zu Köln
    Principal Investigator
  • member's portrait

    Prof. Dr. Benedikt Jahnel

    Technische Universität Braunschweig
    Principal Investigator
  • member's portrait

    Prof. Dr. Wolfgang König

    Weierstrass Institute
    Principal Investigator
  • member's portrait

    Dr. Karl Olof Hallqvist Elias

    Universität zu Köln
    Associated Scientist
  • member's portrait

    Dr. Sanjoy Kumar Jhawar

    Weierstrass Institute
    Associated Scientist
  • member's portrait

    Dr. András Tóbiás

    Budapest University of Technology and Economics
    Associated Scientist
  • member's portrait

    M. Sc. Ahn Duc Vu

    Weierstrass Institute
    Associated Scientist
  • member's portrait

    Dr. Alexander Zass

    Weierstrass Institute
    Associated Scientist

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