About  Research  Events  People  Reports  Alumni  Contact  Home


SUMMARY The main theme of the workshop is "Variational methods
in probability theory and statistical physics", with focus on the application of
large deviation theory to interacting particle systems, including gradient
flows, polymers and disordered systems. ORGANISERS
INVITED SPEAKERS
Monday March 14
Tuesday March 15
Wednesday March 16
Thursday March 17
Friday March 18
***************************************************************************************************************************************** ABSTRACTS Stefan Adams Sample path large deviations and scaling limits for weakly pinned integrated random walks We study scaling limits and the corresponding large deviation principle of the integrated random walk perturbed by an attractive force towards the origin. In particular we analyze the critical situation that the rate function admits more than one minimiser leading to concentration of measure problems. The integrated random represents interface models with Laplacian interaction. Erwin Bolthausen Localization properties of random surfaces with pinning We present two recent results on random surfaces with local pinning The
first one (joint work with T. Chyonobu and T. Funaki) on a classical
gradient interface model at a critical parameter and the second one (jointworkd
with A. Cipriani, N. Kurt) on the decay of correlations in a membrane model. Anton Bovier/Patrick Müller Hydrodynamic limits, propagation of chaos and large deviations in local meanfield models with unbounded spins We consider systems of stochastic differential
equations that describe the dynamics of unbounded spinsystems where spins
interact via longrange spatially variable interactions. We prove the
convergence Paul Chleboun Large deviations of the empirical current in zerorange processes on a ring We examine atypical current fluctuations in totally asymmetric zerorange
processes in one dimension with periodic boundary conditions. For large
systems, by calculating the JensenVaradhan action functional, we are able
to predict the time dependent optimal profiles which realise currents below
the typical value. Under certain conditions on the jump rates, we
demonstrate that these systems can exhibit a dynamical phase transition.
Above a critical nontypically current the optimal macroscopic density
profile is given by a traveling wave with a shock and antishock pair, while
rare events below the critical current are realised by condensed
configurations, in which a positive fraction of all the particles accumulate
on a single site in the thermodynamic limit. Heuristics are supported by
simulations using 'sensemble' cloning methods. Jin Feng On the metric nature of some HamiltonJacobi equations for infinite particles In this talk, a class of HamiltonJacobi PDEs in the
space of probability measures will be formulated as equations in length
metric spaces. These equations arise from both statistical mechanics as well
as continuum mechanics applications. We develop an abstract wellposedness
theory by introducing a new notion of viscosity solution. Davide Gabrielli Discrete and continuous variational problems for current fluctuations I will first discuss current fluctuations for
interacting particle systems in the hydrodynamic scaling limit and the
related variational principles. In particular I will discuss the additivity
principle, the dynamic approach and the existence of dynamic phase
transitions. Giambattista Giacomin Pinning and disorder relevance for the lattice Gaussian free field in dimension three or more I will present recent results on the localization transition for a Gaussian
free field on Z_{d} , d≥3, interacting with a quenched disordered
substrate that acts on the interface when the interface height is close to zero.
The substrate has the tendency to localize or repel the interface at different
sites and one can show that a localizationdelocalization transition takes place
when varying the average pinning potential Stefan Grosskinsky We consider a zerorange process with jump rates decreasing with the
occupation number, which is known to exhibit a condensation phenomenon where a
finite fraction of all particles concentrates on a single lattice site. We
derive a scaling limit for the asymptotic stationary dynamics of the condensate
location in the thermodynamic limit on a onedimensional torus. Our proof
follows previously developed methods using potential theory and a martingale
approach, which have been applied to zerorange processes on finite lattices.
The main challenge and novelty of our paper arises from the absence of attractor
states which complicates the proof of equilibration within metastable wells and
requires a coupling argument to get uniform bounds on exit rates from wells. Sabine Jansen Surface energy and transfer operators for a chain of atoms at low temperature We analyze the surface Gibbs free energy and the
transfer operator for a chain at atoms in the limit where the temperature goes
to zero. The interaction potential is of LennardJones type. Our main results
are: Wolfgang König A variational formula for the free energy of an interacting manybody system We consider N bosons in a box in the ddimensional space in a large box under the influence of a mutually repellent pair potential. The particle density is kept fixed and positive. Our main result is the identification of the limiting free energy at positive, sufficiently high temperature in terms of an explicit variational formula. The thermodynamic equilibrium is described by the symmetrised trace of the negative exponential of the corresponding Hamilton operator. The wellknown FeynmanKac formula reformulates this trace in terms of N interacting Brownian bridges. Due to the symmetrisation, the bridges are organised in an ensemble of cycles of various lengths. The novelty of our approach is a description in terms of a marked Poisson point process whose marks are the cycles. This allows for an asymptotic analysis of the system via a largedeviation analysis of the stationary empirical field. The resulting variational formula ranges over random shiftinvariant marked point fields and optimizes the sum of the interaction and the relative entropy with respect to the reference process. Our formula is not able to express the unboundedly long cycles; as a result we derive only lower and upper bounds. Our results and their shortcomes are at the heart of BoseEinstein condensation. Tom Kurtz The semigroup approach to large deviation theorems for Markov processes The semigroup approach to proving large deviation results for Markov processes developed in Feng and Kurtz (2006) will be outlined and illustrated by application to models arising in systems biology. Carlangelo Liverani Large deviations and metastability in deterministic systems Lots of results are available for large deviations and metastability in random particle systems. On the contrary next to nothing is known when the dynamics is deterministic and the only randomness lies in the initial condition. I will describe a simple (but highly non trivial) system in which precise results can be obtained. this can be considered as the zero step in the direction of studying some Hamiltonian interacting particles systems. Christian Maes The physics in large deviation functionals We give some physics interpretation to static and dynamic large deviation functionals that have appeared in statistical mechanics. For equilibrium, the macroscopic fluctuations are directly related to heat and work. For nonequilibrium, there are relations with entropy production rates, with dynamical activity and statistical forces in general. Angela Stevens Directed cell motion and a hydrodynamic limit for chemotaxis In this talk the first equation of a chemotaxis system is derived as a hydrodynamic limit from a stochastic interacting many particle system on the lattice. The cells do interact with attractive chemical molecules and among themselves on the same lattice site. The chemical environment is assumed to be stationary with a slowly varying mean. This results in a nontrivial macroscopic chemotaxis equation for the cells. Directed cell motion  like chemotaxis  is induced by polymerization and
depolymerization of actin filaments within the cellular cytoskeleton. If
time permits, a onedimensional hyperbolicparabolic model for the dynamics
of the actin cytoskeleton is derived and the emergence of Dirac measures for
the respective filament tips is discussed. Florian Theil Orientational order in two dimensions A classic phenomenon is Statistical Mechanics is the emergence of crystalline phases at low temperature. Until recently not much was known about this problem in the case of atomistic systems with unbounded degrees of freedom. I will explain the link between crystal formation and orientational order. Then I will demonstrate that orientational order emerges in many realistic twodimensional systems. Balint Toth Superdiffusive bounds for selfrepelling motions in low dimension I will give a survey of the resolvent method for obtaining bounds on
diffusivity of random motions. This powerful method was initiated by
LandimQuastelSalmhoferYau (2004) and Yau (2004) and leads to variational
poblems. So it fits well to the central theme of this workshop. I will show
some applications to diffusion in random drift field and selfrepelling
Brownian polymer. Ofer Zeitouni Large deviations for the twodimensional twocomponent plasma We derive a large deviations principle for the twodimensional twocomponent plasma in a box. As a consequence, we obtain a variational representation for the free energy, and also show that the macroscopic empirical measure of either positive or negative charges converges to the uniform measure. Johannes Zimmer Nonlinear diffusion: from particle models to gradient flows This talk will study scalebridging from a thermodynamic perspective,
focusing on gradient flows. We discuss the interplay between particle models
and their thermodynamic description at hand of a class of nonlinear
diffusion equations. It will first be shown how an underlying particle model
can reveal an underlying (geo)metric structure of the governing PDE,
notably a gradient flow setting for a class of nonlinear diffusion
equations. Large deviation arguments will be discussed, and it will be
sketched how this can link mesoscopic fluctuations and stochastic PDEs in a
way that can allow to derive stochastic "corrections" for deterministic PDEs.
PRACTICAL INFORMATION ● VenueEurandom, 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).
● RegistrationRegistration is free, but compulsory for speakers and participants. Please follow the link: REGISTRATION PAGE
● AccommodationFor 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.
● TravelFor 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&12The meetingroom 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 SecretariatUpon 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 daytoday running of the conference: registration, issuing certificates and receipts, etc.
● CancellationShould 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 noshow fee of 30 euro.
● ContactMrs. Patty Koorn, Workshop Officer, Eurandom/TU Eindhoven, koorn@eurandom.tue.nl SPONSORSThe organisers acknowledge the financial support/sponsorship of:
Last updated
100316,
