European Institute for Statistics, Probability, Stochastic Operations Research
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March 7-11, 2016



Large Deviations for Interacting Particle Systems
and Partial Differential Equations


(part of SAM "Probability and Analysis")







The thirteenth edition of the Young European Probabilists (YEP) workshop focusses on "Large Deviations for Interacting Particle Systems and Partial Differential Equations".
The program consists of three mini courses in the morning sessions intended for young researchers with a background at the interface between analysis and stochastics, and 30-minute presentations by invited speakers in the afternoon sessions.

The YEP XIII brings together many junior and some senior scientists whose research interests are strongly related to the selected topic. This mix of researchers aims at giving a special, open atmosphere which in the past has proven to be very fruitful for fostering discussions among the participants.


Luca Avena University of Leiden
Roberto Fernandez Utrecht University
Francesca Nardi TU Eindhoven




Francesco Caravenna University of Milan, Bicocca Polynomial chaos and scaling limits of disorderded systems - link 1 ; link 2 ; link 3
Antoine Gloria ULB Brussels A path-wise theory of fluctuations in stochastic homogenization
Jan Maas IST Austria Discrete curvature, gradient flows and interacting particle systems



Marton Balazs University of Bristol
Gioia Carinci TU Delft
Giacomo Di Gesů CERMICS, Ecole des Ponts
Sören Dobberschütz University of Copenhagen
Laure Dumaz Cambridge University
Clement Erignoux CMAP, Ecole Polytechnique
Carlos Perez Espigares University of Modena
Max Fathi Berkeley University
Patricia Goncalves PUC, Rio de Janeiro
Chris Janjigian Madison, Wisconsin
Richard Kraaij TU Delft
Mauro Mariani La Sapienza, Rome
Georg Menz UCLA
Chiranjib Mukherjee NYU
Pierre Nyquist Brown University
Christophe Poquet Lyon 1 Univeristy
Michiel Renger WIAS Berlin
Andre Schlichting University of Bonn
Marielle Simon INRIA
Willem van Zuijlen Leiden University



Monday March 7

09.00 - 09.20 Registration  
09.20 - 09.30 Opening Remco van der Hofstad (Eurandom/TUe)  
09.30 - 11.00 Mini course Jan Maas (I)  
11.00 - 11.30 Break    
11.30 - 13.00 Mini course Francesco Caravenna (I)  
13.00 - 15.00 Lunch    
15.00 - 15.35   Michiel Renger  
15.35 - 16.10   Richard Kraaij  
16.10 - 16.30 Break    
16.30 - 17.05   Willem van Zuijlen  
17.05 - 17.40   Chiranjib Mukherjee  

Tuesday March 8

09.30 - 11.00 Mini course Antoine Gloria (I)  
11.00 - 11.30 Break    
11.30 - 13.00 Mini course Jan Maas (II)  
13.00 - 15.00 Lunch    
15.00 - 15.35   Patricia Goncalves  
15.35 - 16.10   Marton Balasz  
16.10 - 16.30 Break    
16.30 - 17.05   Marielle Simon  
17.05 - 17.40   Christophe Poquet  
18.30 - Conference Dinner    

Wednesday March 9

09.30 - 11.00 Mini course Francesco Caravenna (II)  
11.00 - 11.30 Break    
11.30 - 13.00 Mini course Antoine Gloria (II)  
13.00 - 15.00 Lunch    
15.00 - 15.35   GioiaCarinci  
15.35 - 16.10   Pierre Nyquist  
16.10 - 16.30 Break    
16.30 - 17.05   Carlos Perez Espirages  
17.05 - 17.40   Sören Dobberschütz  

Thursday March 10

09.30 - 11.00 Mini course Jan Maas (III)  
11.00 - 11.30 Break    
11.30 - 13.00 Mini course Francesco Caravenna (III)  
13.00 - 15.00 Lunch    
15.00 - 15.35   Giacomo Di Gesu  
15.35 - 16.10   Georg Menz  
16.10 - 16.30 Break    
16.30 - 17.05   Max Fathi  
17.05 - 17.40   André Schlichting  

Friday March 11

09.00 - 10.30 Mini course Antoine Gloria (III)  
10.30 - 10.45 Break    
10.45 - 11.20   Laure Dumaz  
11.20 - 11.55   Mauro Mariani  
11.55 - 12.00 Break    
12.00 - 12.35   Clement Erignoux  
12.35 - 13.10   Chris  Janjigian  
13.10 - 14.00 "Take away lunch"    




Márton Balázs

How to initialise a second class particle?

Since the beautiful paper of Ferrari and Kipnis we know that the second class particle of simple exclusion chooses a uniform random direction in the rarefaction fan. The extremely elegant proof is based, among other ideas, on the fact that increasing the parameter of a Bernoulli distribution can be done by adding or not adding an extra (that is, second class) particle to a site.
Generalising the argument for other models is non-trivial for two reasons. (1) Increasing the parameter of the marginal of a stationary distribution often cannot be done just by adding or not adding a single second class particle. (2) There are lots of choices to make for starting a second class particle when we can have more than one particles on a site. How should we pick our choice?
I will show how to overcome both these issues at once by introducing a coupling measure of possibly negative weights which nevertheless serves as a proper probability distribution to start a second particle from. This distribution seems to be ”the canonical one” in many ways. In particular it allows to extend Ferrari and Kipnis’ results to a vast class of particle systems. I will also illustrate curious second class particle behaviours via some fun examples.
(joint work with Attila Lszl Nagy)


Gioia Carinci

Microscopic models for Free Boundary Problems

Macroscopic laws of transport are described by PDE's. Their derivation from microscopic models of interacting particles is a recurrent theme in non-equilibrium statistical mechanics literature. When the microscopic system is open, there are several mechanisms to couple the system with the external forces. In this talk I will present a class of systems where the interaction with the exterior takes place in correspondence of a free boundary.

Giacomo Di Gesů

Analysis of the relaxation time of a large bistable particle system at low temperature

A large system of strongly coupled diffusions on unbounded state space moving in a double-well potential is considered. This system can be seen as a spatially discrete approximation of the stochastically perturbed Allen-Cahn equation on the one-dimensional torus, which is a basic and widely studied stochastic partial differential equation.
In the small temperature regime the typical picture of a metastable dynamics emerges: the system quickly reaches a local equilibrium in one of the two wells, depending on its initial condition; this state endures for a very long time, until a sufficiently large stochastic fluctuation enables the system to overcome the energetic barrier separating the two wells and thus to distribute according to the global equilibrium.
I will present some results, obtained in collaboration with Dorian Le Peutrec, which quantify the mentioned slowdown in the relaxation to equilibrium. More specifically, these results concern spectral gap and log-Sobolev constant in regimes of low temperature and large number of particles.

Sören Dobberschütz

Boundary conditions at the interface between a liquid and a porous medium

The boundary conditions between a free fluid flow and a flow in a porous medium are of theoretical as well as practical importance in a number of disciplines, for example in reservoir engineering, marine biology and soil chemistry. A classical result is the boundary condition of Beavers-Joseph-Saffman, which requires the fluid’s velocity field to be continuous in the direction normal to the interface. In tangential direction, a jump between the velocities in the free fluid and the porous medium occurs. With experimental evidence dating back to the 1960s, this boundary condition has recently been justified mathematically by Jäger, Mikelić and Marciniak-Czochra - but only for the case of a planar interface. In this talk, we present their method of multiscale matched asymptotic expansion and how it can be generalized to also include the case of a curved porous-liquid interface, giving a generalized boundary condition of Beavers-Joseph-Saffman.


Laure Dumaz

Beta ensembles at high temperature

In this talk, I will introduce random operators describing the continuum limit of beta ensembles (by Ramirez, Valko and Virag). I will show how to derive the behavior of the particles at high temperature thanks to this approach.
(joint work with R. Allez)

Clément Erignoux

Hydrodynamics of a non-gradient model for collective dynamics

Extensive work has been put in the modelling of animal collective dynamics in the last decades, building on the work of ViscekAl (1995). These empirical approaches have unveiled several interesting phenomenon regarding phase transitions and separations. However, most of the theoretical background in collective dynamics modelling relies on mean-field approximations. I will present a lattice model where interactions between partices happen at a purely microscopic level, and describe some of the challenges in the proof of its hydrodynamic limit.


Max Fathi

Ricci curvature  and functional inequalities for interacting particle systems

In this talk, I will present a few results on entropic Ricci curvature bounds for interacting particle systems. These curvature bounds can be used to prove functional inequalities, such as spectral gap bounds and modified logarithmic Sobolev inequalities, which measure the rate of convergence to equilibrium for the underlying dynamic.
(joint work with M. Erbar and J. Maas)

Patricia Goncalves

On the asymptotic behavior of slowed exclusion processes

In this talk I will describe the asymptotic behavior of the symmetric simple exclusion with a slow bond and a particular emphasis will be given on the equilibrium fluctuations of its weakly asymmetric version. Depending on the strength of the asymmetry we see a crossover from the Edwards-Wilkinson universality class to the KPZ universality class.


Chris Janjigian

Large deviations for certain inhomogeneous corner growth models

The corner growth model is a classical model of growth in the plane and is connected to other familiar models such as directed last passage percolation and the TASEP through various geometric maps. In the case that the waiting times are i.i.d. with exponential or geometric marginals, the model is well understood: the shape function can be computed exactly, the fluctuations around the shape function are known to be given by the Tracy-Widom GUE distribution, and large deviation principles corresponding to this limit have been derived. 
This talk considers the large deviation properties of a generalization of the classical model in which the rates of the exponential are drawn randomly in an appropriate way. We will discuss some exact computations of rate functions in the quenched and annealed versions of the model, along with some interesting properties of large deviations in these models.
(joint work with Elnur Emrah)

Richard Kraaij

Large deviations for interacting jump processes via solving a set of Hamilton-Jacobi equations

We revisit the large deviation principle for trajectories of interacting jump processes on a finite state space. We give a new proof based on proving uniqueness of viscosity solutions of a set of associated Hamilton-Jacobi equations. The obtained result extends previously known results obtained via classical change of measure techniques. The method that shows that uniqueness of viscosity solutions leads to the large deviation principle are based on the work by Feng and Kurtz[2006].

Mauro Mariani

Macroscopic fluctuations for random collisional dynamics

I will discuss fluctuations for the current of energy transferred by a large system of particles. The dynamics features random elastic collisions among particles, and the system is in contact with boundary wall at different temperatures.

Georg Menz

The log-Sobolev inwquality unbounded spin systems

The log-Sobolev inequality (LSI) is a very useful tool for analyzing high-dimensional situations. For example, the LSI can be used for deriving hydrodynamic limits, for estimating the error in stochastic
homogenization, for deducing upper bounds on the mixing times of Markov chains, and even in the proof of the Poincaré conjecture by Perelman. For most applications, it is crucial that the constant in the
LSI is uniform in the size of the underlying system. In this talk, we discuss when to expect a uniform LSI  in the setting of unbounded spin systems.

Chiranjib Mukherjee

Occupation measures, compactness and large deviations

In a reasonable topological space, large deviation estimates essentially deal with probabilities of events that are asymptotically (exponentially) small, and in a certain sense, quantify the rate of these decaying probabilities. In such estimates, lower bound for open sets and upper bound for compact sets are essentially local estimates. However, upper bounds for all closed sets often require compactness of the ambient space or stringent technical assumptions (e.g., exponential tightness), which is often absent in many interesting problems which are motivated by questions arising in statistical mechanics (for example, distributions of occupation measures of Brownian motion in the full space Rd). Motivated by problems that carry certain shift-invariant structure, we present a robust theory of “translation-invariant ompactification” of orbits of probability measures in Rd. This enables us to prove a desired large deviation estimates on this “compactified” space. Thanks to the inherent shift- invariance of the underlying problem, we are able to apply this abstract theory painlessly and solve a long standing problem in statistical mechanics, the mean-field polaron problem.
(joint work with S. R. S. Varadhan, Erwin Bolthausen and Wolfgang König)


Pierre Nyquist

A large deviation analysis of some qualitative properties of parallel tempering and infinite swapping algorithms

We review the MCMC method knows as parallel tempering and its so-called infinite swapping limit, both which correspond to a collection of interacting particles. Focusing on infinite swapping we then employ a large deviation analysis and methods from stochastic optimal control to discuss certain qualitative properties. In particular we discuss how symmetry properties of the underlying potential landscape may affect convergence properties and how the rate function identifies those parts of the state space where noise due to sampling has the greatest impact on the overall performance of the algorithms.
(joint work with Jim Doll and Paul Dupuis)


Carlos Perez-Espigares

A weak additivity principle for current statistics in d-dimensions

The additivity principle (AP) allows to compute the current distribution in many one-dimensional (1d) nonequilibrium systems. Here I will extend this conjecture to general d-dimensional driven diffusive systems, and validate its predictions against both numerical simulations of rare events and microscopic exact calculations of three paradigmatic models of diffusive transport in d = 2. Crucially, the existence of a structured current vector field at the fluctuating level, coupled to the local mobility, turns out to be essential to understand current statistics in d > 1. I will prove that, when compared to the straightforward extension of the AP to high-d, the so-called weak AP always yields a better minimizer of the macroscopic fluctuation theory action for current statistics.


Christophe Poquet

Random long time dynamics in the stochastic Kuramoto model

The stochastic Kuramoto model is a toy model used to study synchronization phenomena. It consists in a population of N rotators with mean field interaction, each rotator being perturbed by a Brownian noise and possessing its own natural frequency of rotation. These frequencies are identically distributed and drawn independently, and correspond to a second source of randomness for the system (in addition to the thermal noise), called disorder.
On finite time intervals [0,T] and in the limit of infinite population the model is described by a PDE of Fokker-Planck type. This limit model undergoes a synchronization type phase transition: when the interaction is strong enough this PDE admits a stable curve M (in fact a circle), corresponding to the synchronization of the rotators around a synchronization center that rotates at constant speed.
When the distribution of the disorder is symmetric, this speed is equal to zero. We will see that in that case, when the size N of the population is large but finite, disorder-induced traveling-waves appear on the time scale N^{1/2}, with a speed given by the asymmetry of the finite-size draw of the disorder.
(joint work with L. Bertini, G. Giacomin and E. Luçon)

Michiel Renger

Large deviations for reacting particle systems: the empirical and ensemble process

We study the empirical measure of particles that can react randomly to form new particles. The resulting Markov processes are typically used as microscopic models for the deterministic reaction rate equation. In a similar fashion, but one level higher, one can study the empirical measure of the empirical measure, which then converges to the solution of a Liouville transport equation as both the number of particle systems and the number of particles in each system go to infinity. We are after large deviations for both processes. It turns out that the spaces of bounded variation provide natural topologies for both processes. In fact, the usage of these topologies in large deviations is not very common and therefore, hopefully, interesting in its own right.

André Schlichting

Discrete gradient flow structures for mean-field systems

In this talk, we show that a family of non-linear mean-field equations on discrete spaces can be viewed as a gradient flow of a free energy functional with respect to a certain metric structure, we make explicit. We also prove that this gradient flow structure arises as the limit of the gradient flow structures of a natural sequence of N-particle dynamics, as N goes to infinity.
We will address work in progress and open questions regarding the displacement convexity of the limit and the N-particle system exemplified for the Curie-Weiss mean-field spin system.
(joint work with M. Erbar (U Bonn), M. Fathi (UC Berkeley), V. Laschos (WIAS Berlin); arXiv: 1601.08098)


Marielle Simon

Equilibrium fluctuations for one-dimensional conservative systems with degenerate rates

The study of fluctuations for one-dimensional conservative systems (like, for instance, exclusion-type processes) often involves the so-called Boltzmann-Gibbs principle which states that the space-time fluctuations of any local field associated to a conservative mode can be written as a linear functional of the conservative field. A second-order Boltzmann-Gibbs principle has been introduced in 2014 by Gonçalves and Jara in order to investigate the first-order correction of this limit, in which case is given by a quadratic functional of the conservative field. The proof of that result was based on a multiscale analysis assuming that the underlying particle system is of exclusion type and for which a spectral gap inequality holds. In collaboration with  O. Blondel and P. Gonçalves, we gave a new proof of that second-order Boltzmann-Gibbs principle in order to fit microscopic dynamics with kinetic constraints, which are not ergodic and provide blocked states. 


Willem van Zuijlen

Gibbsianness related to minimisers of a large deviation rate function

In this talk I discuss dynamical Gibbs-non-Gibbs transitions for mean-field spin systems. Gibbsianness is related to the number of global minimisers of a large deviation rate function. A unique global minimiser implies Gibbsianness while multiple imply non-Gibbsianness. I explain the background of this relation and list possible scenarios when the spins perform independent Brownian motions.
(joint work with Frank den Hollander and Frank Redig)





Eurandom, Mathematics and Computer Science Dept, TU Eindhoven,

Den Dolech 2, 5612 AZ  EINDHOVEN,  The Netherlands

Eurandom is located on the campus of Eindhoven University of Technology, in the Metaforum building (4th floor) (about the building). The university is located at 10 minutes walking distance from Eindhoven main railway station (take the exit north side and walk towards the tall building on the right with the sign TU/e).
Accessibility TU/e campus and map.




Registration is closed.




For invited participants, we will take care of accommodation. Other attendees will have to make their own arrangements.

We have a preferred hotel, which can be booked at special rates. Please email Patty Koorn for instructions on how to make use of this special offer.

For other hotels around the university, please see: Hotels (please note: prices listed are "best available"). 

More hotel options can be found on the webpages of the Tourist Information Eindhoven, Postbus 7, 5600 AA Eindhoven.



For those arriving by plane, there is a convenient direct train connection between Amsterdam Schiphol airport and Eindhoven. This trip will take about one and a half hour. For more detailed information, please consult the NS travel information pages or see Eurandom web page location.

Many low cost carriers also fly to Eindhoven Airport. There is a bus connection to the Eindhoven central railway station from the airport. (Bus route number 401) For details on departure times consult http://www.9292ov.nl

The University  can be reached easily by car from the highways leading to Eindhoven (for details, see our route descriptions).


      Conference facilities : Conference room, Metaforum Building  MF11&12

The meeting-room is equipped with a data projector, an overhead projector, a projection screen and a blackboard. Please note that speakers and participants making an oral presentation are kindly requested to bring their own laptop or their presentation on a memory stick.


      Conference Secretariat

Upon arrival, participants should register with the workshop officer, and collect their name badges. The workshop officer will be present for the duration of the conference, taking care of the administrative aspects and the day-to-day running of the conference: registration, issuing certificates and receipts, etc.



Should you need to cancel your participation, please contact Patty Koorn, the Workshop Officer.

There is no registration fee, but should you need to cancel your participation after January 2, 2014, we will be obliged to charge a no-show fee of 30 euro.



Mrs. Patty Koorn, Workshop Officer, Eurandom/TU Eindhoven, koorn@eurandom.tue.nl



The organisers acknowledge the financial support/sponsorship of:







Last updated 20-04-16,
by PK

 P.O. Box 513, 5600 MB Eindhoven, The Netherlands
tel. +31 40 2478100  
  e-mail: info@eurandom.tue.nl