Random Point Processes in Statistical Physics

13:00-13:30 Registration
13:30-13:45 Welcome Address
13:45-14:45 Scientific Talk: David Dereudre
14:45-15:45 Scientific Talk: Michael Klatt
15:45-16:15 Coffee Break
16:15-17:15 Scientific Talk: Christof Külske
17:15-18:15 Scientific Talk: Günter Last

Thursday

9:00-10:30 Minicourse I: Wolfgang König
10:30-11:00 Coffee Break
11:00-12:30 Minicourse II: Aernout van Enter
12:30-13:30 Lunch Break
13:30-14:30 Scientific Talk: James Lutsko
14:30-15:30 Scientific Talk: Wioletta Ruszel
15:30-16:00 Coffee Break
16:00-17:00 Scientific Talk: Alexander Zass
17:00-18:00 Discussion on Math-Phys Notions
18:30-20:30 Conference Dinner

Friday

9:00-10:30 Minicourse I: Wolfgang König
10:30-11:00 Coffee Break
11:00-12:30 Minicourse II: Aernout van Enter
12:30-13:30 Lunch Snack

Audience

The workshop is designed as an inperson meeting without additional streaming. There is an upper bound of 30 participants and preference will be given to members of the SPP2265.

Participants

Luisa Andreis
Irene Ayuso Ventura
Friedemann Brockmeyer
Matteo D'Achille
David Dereudre
Matthias Eckardt
Tejas Iyer
Benedikt Jahnel
Jonas Jalowy
Sanjoy Kumar Jhawar
Michael Klatt
Wolfgang König
Christof Külske
Vaios Laschos
Günter Last
James Lutsko
Hartmut Löwen
Robert Patterson
Wioletta Ruszel
Cédric Schoonen
Thais Silva
András Tóbiás
Anh Duc Vu
Marwan Wehaiba El Khazen
Wei Xu
Alexander Zass
Aernout van Enter
Mandala von Westenholz

Conference Dinner

Titles, Abstracts and Slides

Aernout van Enter: Gibbs measures on lattice systems, discreteness and continuity.
I will discuss Gibbs measures and various discrete vs continuous aspects of them. Among other things, I will mention some examples how the study of lattice models can inform that of continuum models. We will discuss various classes of examples of measures where the characterisation of measures as Gibbs measures in terms of continuity properties can be checked and has been the subject of recent studies. In particular we will explore the distinction between Gibbs and g-measures, and the related issue of local and global Markov properties. I will describe how the implementation of the Renormalisation Group, coarse-graining. thinning and decimation transformations on Gibbs measures has led to various obstructions. I will also discuss stochastic evolutions and how modelling `'heating" (raising the temperature) can lead to measures where the notion of temperature becomes ill-defined.
Wolfgang König: Many-body systems and the interacting Bose gas
In the first part, we consider a many-body system with pair interaction of Lennard-Jones type and discuss it from the viewpoint of large-deviations theory for point processes. In a particular regime with high diluteness at low temperature, we are able to derive an explicit picture of the particle configuration. In the second part, we start from the Hamilton operator of the interacting Bose gas and derive a representation in terms of a marked point process. We analyse the free energy with the help of large-deviation theory for marked point processes and discuss the possible appearance of macroscopic structures.
David Dereudre: Number-rigidity and beta-circular Riesz gas
For an inverse temperature beta>0, we define the beta-circular Riesz gas on Rd as any microscopic thermodynamic limit of Gibbs particle systems on the torus interacting via the Riesz potential g(x) = 1/|x|^s. We focus on the non integrable case d-10, the existence of a beta-circular Riesz gas which is NOT number-rigid. Recall that a point process is said number rigid if the number of points in a bounded Borel set Delta is a function of the point configuration outside Delta. It is the first time that the non number-rigidity is proved for a Gibbs point process interacting via a non integrable potential. We follow a statistical physics approach based on the canonical DLR equations.
Michael Klatt: Hyperuniformity in physics and mathematics
What do the eyes of chicken, Coulomb gases, and the prime numbers have in common? In all of these systems, an anomalous suppression of large-scale density fluctuations has been found, known as disordered hyperuniformity. This talk will take a look at this rapidly growing research topic from both the point of view of mathematics and physics. First, this will include a brief overview, from basic definitions to recent progress. Then, as a specific example, the talk will show how a stable matching between perfect order (represented by a lattice) and complete spatial randomness (i.e., the Poisson point process) results in a hyperuniform point process [1]. The talk will also touch upon the relation to rigidity phenomena [2] and higher-order moments of the so-called number distribution [3]. [1] Klatt, Last, Yogeshwaran. Random Struct. Algor. 57, 439 (2020); [2] Klatt, Last. arXiv:2008.10907 (2020); [3] Torquato, Kim, Klatt. Phys. Rev. X 11, 021028 (2021)
Christof Külske: Hidden phase transitions in thinned point clouds
Thinning transformations play an important role in the study of point particles in continuous space. We consider a discrete analogue of such a setup, namely the independent Bernoulli lattice field under projection to isolated sites. This transformation comes with a natural companion, namely the projection to non-isolated sites. We describe recent results on the regularity/irregularity of such maps on the level of infinite-volume measures, and how they are linked to absence/presence of internal phase transitions. Joint work with Nils Engler and Benedikt Jahnel.
Günter Last: Disagreement coupling of finite Gibbs processes
We will present a general version of the so-called disagreement coupling of finite Gibbs processes based on a (non-dynamical) Poisson embedding. The thinning version of this coupling was introduced in a seminal paper by van den Berg and Maes (1994) in a discrete setting and was then extended to the continuum by Hofer-Temmel (2019). Assuming the underlying Poisson process to be subcritical in a suitable sense, we will provide two applications to repulsive Gibbs processes. The first is exponential decorrelation and the second are new uniqueness citeria for Gibbs distributions based on a non-negative pair potential. The talk is based on joint work with Steffen Betsch and Moritz Otto.
James Lutsko: Understanding crystallization using density functional theory and fluctuating hydrodynamics
The theoretical description of any first order phase transition requires an understanding of both thermodynamics and dynamics. Crystallization is particularly challenging due to the inhomogeneous nature of the crystalline state. I will discuss the use of classical Density Functional Theory, which gives a realistic ab initio description of the thermodynamics of solids, in combination with fluctuating hydrodynamics to give a fully nonequilibrium description of crystal nucleation. It will be shown how Classical Nucleation Theory can be recovered from this framework as a natural approximation. Application of the full theory to crystallization of particles interacting via the Lennard-Jones potential leads to several non-classical effects including long-wavelength, low-amplitude density fluctuations as nucleation precursors and a complex, multistep nucleation pathway leading to the solid state.
Wioletta Ruszel: Random field induced order in 2d
In this talk we will discuss random field induced ordering. In particular we shall prove that a classical O(2) model subjected to a weak i.i.d. Gaussian field pointing in a fixed direction exhibits residual magnetic order on the square lattice Z^2 and moreover aligns perpendicular to the random field direction. This type of transition is also referred to as of spin-flop type. Our approach is based on a multi-scale Peierls contour argument developed. This is joint work with N.Crawford (Technion, Israel).
Alexander Zass: Interacting diffusions as marked Gibbs point processes
The motivation for this talk comes from seeing a class of infinite-dimensional diffusions in interaction as marked point configurations: the starting points belong to R^d, the marks are the paths of Langevin diffusions, and the interaction between two diffusions is given by the integration of a pair potential along their paths. In the first part of the talk, we use the entropy method to show the existence of an infinite-volume Gibbs point process for a general mark space and a general interaction with unbounded range. This result can be applied not only to the path-space pair-potential setting, but also to stochastic-geometry multi-body examples, like the area-interaction process. In the second part of the talk, we present a uniqueness result in the general pair-potential setting, obtained by using cluster expansion techniques.

Venue

The venue of the Workshop is the Harnack-Haus at Ihnestraße 16-20, 14195 Berlin-Dahlem.
Most of the event will take place in the Meitner-Hörsaal.

The hygiene concept of the venue is available here. The organisers have the right to take additional measures.

Getting there

The venue is close to the U-Bahn station Freie Universität (Thielplatz), on the U3 line.

To reach it from the Zoologischer Garten train station, you can take the U9 towards Rathaus Steglitz and change at Spichernstrasse.

Accommodation

The organisers have reserved hotel rooms at the Motel One on Kurfürstendamm. During the registration process, you will be able to request us to book a room for you. Self-organized housing is possible, and members of SPP2265 will be reeimbursed if the hotel price stays within reasonable bounds (e.g., below 100 Euros per night).

Contact

If you have any questions, please do not hesitate to

at Benedikt.Jahnel@wias-berlin.de.

Homepage of the SPP2265.

Berlin, June 29 - July 1, 2022

Programme

Minicourses

Aernout van Enter

Wolfgang König

Preliminary schedule