Equilibrium and Non-equilibrium Statistical Mechanics A conference in honor of François Dunlop

Liste des Contributions

21. Introduction

François Dunlop

08/04/2019 10:40

18. One-sided versus two-sided dependence.

Aernout van Enter

08/04/2019 11:00

Stochastic systems can be parametrised by time (like Markov chains),in which conditioning is one-sided (the past)or by one-dimensional space (like Markov fields), where conditioning is two-sided (right and left).I will discuss some examples, in particular generalising this to g-measures versus Gibbs measures, where, instead of a Markovian dependence, the weaker property of continuity (in the...

8. Gibbs states for (long-range) Ising models.

Loren Coquille

08/04/2019 11:50

I will review old and present new results on standard and long-range Ising models in dimension $1$, $2$ and $3$. I shall focus on fluctuations or rigidity of interfaces at low temperature, in the coexistence regime.
Based on works in collaboration with Y. Velenik (Geneva) on one hand, and A. van Enter (Groningen), A. Le Ny (Paris) and W. Ruszel (Delft) on the other hand.

12. Wetting, disordered pinning and layering for discrete random interfaces

Hubert Lacoin

08/04/2019 14:10

Solid-on-Solid (SOS) is a simplified surface model which has been introduced to understand the behavior of Ising interfaces in $\mathbb Z^d$ at low temperature. The simplification is obtained by considering that the interface is a graph of a function $\phi$, $\mathbb Z^{d-1} \to \mathbb Z$. In the present talk, we study the behavior of SOS surfaces in $\mathbb Z^2$ constrained to remain...

17. Shaken dynamics for 2d Ising model.

Elisabetta Scoppola

08/04/2019 15:00

We define a random dynamics which is a composition of two steps of parallel updating with interaction in opposite directions. The invariant measure of this dynamics turns out to be the marginal of the Gibbs measure of an Ising model on hexagonal graphs. The shaken dynamics can be applied to study the effect of earth tides on earthquakes.

10. Elliptic dimers and genus $1$ Harnack curves.

Béatrice de Tilière

08/04/2019 15:50

15. Universality for Kinetically Constrained Spin Models.

Fabio Martinelli

09/04/2019 09:00

Kinetically constrained models (KCM) are reversible interacting particle systems with continuous time Markov dynamics of Glauber type, which have been extensively used in the physics literature to model the liquid-glass transition, a major and longstanding open problem in condensed matter physics. They also represent a natural stochastic (and non-monotone) counterpart of the family of cellular...

4. Hydrodynamic limit for a facilitated exclusion process.

Oriane Blondel

09/04/2019 09:50

We show a hydrodynamic limit for the exclusion process on $\mathbb Z$ in which a particle can jump to the right only if it has a particle to its left and vice-versa. This process has an active/inactive phase transition at density $\frac{1}{2}.
Joint work with Cément Erignoux, Makiko Sasada and Marielle Simon.

19. Kinetically constrained models in random environments

Assaf Shapira

09/04/2019 11:00

Kinetically constrained models are a family of interacting particle
systems used by physicists in order to study the liquid-glass
transition. They are characterized by a very simple non-interacting equilibrium, but their dynamics is slowed down by local kinetic constraints, leading to highly non-trivial behavior of time scales. We will discuss these time scales when adding quenched...

9. Fick's law with phase transitions.

Anna De Masi

09/04/2019 11:50

The context is the Fick's law where a stationary current flows in a system driven by the boundaries which are put in contact with suitable reservoirs. This is a much studied problem but only recently together with Olla and Presutti I have obtained results in models with phase transition I will present these models where the stationary non equilibrium distribution is known explicitly and...

5. Chaos propagation for balls into bins dynamics.

Nicoletta Cancrini

09/04/2019 13:50

We consider $N$ balls and $L$ bins. Initially the balls are randomly placed into the bins. At each time a ball is taken from every non empty bin. Then all the drawn balls are placed into the bins according to a definite law. The evolution is a Markov chain. The model is an interacting particle system with parallel updating so it is not reversible. We give conditions under which propagation of...

1. Hydrodynamics and non-equilibrium stationary states for diffusive systems of conversation laws

Stefano Olla

09/04/2019 14:40

We consider one dimensional dynamics of interacting particles that have more conserved quantities that evolve macroscopically in the same diffusive time scale, and their macroscopic evolution is governed by a system of coupled diffusive equations. Their non-equilibrium stationary states, driven by heat bath and external forces, present interesting phenomena like up-hill diffusion, negative...

7. Time scales in some large population birth and death processes, quasi stationary distribution and resilience.

Pierre Collet

09/04/2019 15:50

With S.Meleard and J.-R.Chazottes we consider a birth and death process with one or several species depending on a (large) parameter giving the scale of the populations sizes. Assuming there is a unique globally attracting nontrivial fixed point for the rescaled infinite population dynamical system, we investigate (under some hypothesis) the time scale of global extinction and the existence...

6. Microscopic stochastic particle models for Fick and Fokker- Planck diffusion equations

Emilio Cirillo

10/04/2019 09:00

Diffusion in not homogeneous media can be described both by the Fick and the Fokker-Planck diffusion equation. The question whether one of the two description has to be considered the correct one is often debated in the scientific literature. Using a microscopic approach, we show that both the descriptions are reasonable and that they correspond to different realizations of spatial...

14. Statistical forces and stabilization out-of-equilibrium.

Christian Maes

10/04/2019 09:50

We discuss the nature of induced forces on a probe coupled to a nonequilibrium medium. We show how stabilization of fixed points may be achieved because of nonequilibirum effects.

11. Stochastic homogenization in amorphous media and applications to Mott variable range hopping.

Alessandra Faggionato

10/04/2019 11:00

By extending the method of 2-scale convergence we prove an homogenization theorem of difference operators given by Markov generators of random walks on random marked simple point processes with symmetric jump rates. Using this theorem, we derive two further results: (i) the hydrodynamic limit of the exclusion process given by multiple random walks with hard-core interaction; (ii) the...

16. Glassy states of the Ising model on trees and Lobachevsky plane.

Senya Shlosman

10/04/2019 11:50

I will explain that on trees and on Lobachevsky, the Ising model has a huge continuum of extremal states. As a result, the free state of the Ising model below the spin-glass temperature has a structure of a spin-glass state: it is a mixture of continuum many extremal states.
Joint work with D. Gandolfo, Ch. Maes, and J. Ruiz.

3. Random walk in a non-integrable random scenery time.

Alessandra Bianchi

10/04/2019 14:10

In this talk we consider a one-dimensional process in random
environment, also known in the physical literature as Levy-Lorentz gas. The environment is provided by a renewal point process that can be seen as a set of randomly arranged targets, while the process roughly describes the displacement
of a particle moving on the line at constant velocity, and changing direction at the targets...

13. The Discrete Non Linear Schroedinger Equation: an example of inequivalence between statistical ensembles.

Roberto Livi

10/04/2019 15:00

The dynamics of the DNLSE is characterized by peculiar featuresin the region of parameter space above the line at infinite temperature:the deterministic version exhibits multi-breather states,
lasting over astronomical times, while the stochastic (conservative)
evolution yields a coarsening dynamics to an infinite temperature
lattice, with a superimposed giant breather collecting a finite...

2. Large deviations and concentration of scaling limits for $ (1+1) $ dimensional fields with Laplacian interaction with pinning and wetting

Stefan Adams

We study scaling limits and corresponding large deviation
principles of random fields perturbed by an attractive force towards the origin and/or by hard-wall (wetting) constraints. In particular, we analyse the critical situation that the rate function admits more than one minimiser leading to a concentration of measure problems.
Our models are in fact interface models with Laplacian...