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The thirteenth edition of the Young European
Probabilists (YEP) workshop focusses on "Large Deviations for Interacting
Particle Systems and Partial Differential Equations".
INVITED SPEAKERS (confirmed)
Monday March 7
Tuesday March 8
Wednesday March 9
Thursday March 10
Friday March 11
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.
Microscopic models for Free Boundary Problems
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.
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.
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.
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.
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.
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.
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.
Large deviations for interacting jump processes via solving a set of Hamilton-Jacobi equations
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.
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
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.
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.
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.
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.
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.
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.
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.
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
(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
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, firstname.lastname@example.org
The organisers acknowledge the financial support/sponsorship of: