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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.
Monday March 14
Tuesday March 15
Wednesday March 16
Thursday March 17
Friday March 18
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.
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 mean-field models with unbounded spins
We consider systems of stochastic differential
equations that describe the dynamics of unbounded spin-systems where spins
interact via long-range spatially variable interactions. We prove the
Large deviations of the empirical current in zero-range processes on a ring
We examine atypical current fluctuations in totally asymmetric zero-range
processes in one dimension with periodic boundary conditions. For large
systems, by calculating the Jensen-Varadhan 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 non-typically current the optimal macroscopic density
profile is given by a traveling wave with a shock and anti-shock 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 's-ensemble' cloning methods.
On the metric nature of some Hamilton-Jacobi equations for infinite particles
In this talk, a class of Hamilton-Jacobi 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 well-posedness
theory by introducing a new notion of viscosity solution.
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
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 Zd , 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 localization-delocalization transition takes place
when varying the average pinning potential
We consider a zero-range 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 one-dimensional torus. Our proof
follows previously developed methods using potential theory and a martingale
approach, which have been applied to zero-range 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.
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 Lennard-Jones type. Our main results
A variational formula for the free energy of an interacting many-body system
We consider N bosons in a box in the d-dimensional 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 well-known Feynman-Kac 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 large-deviation analysis of the stationary empirical field. The resulting variational formula ranges over random shift-invariant 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 Bose-Einstein condensation.
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.
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.
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.
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 non-trivial 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 one-dimensional hyperbolic-parabolic model for the dynamics
of the actin cytoskeleton is derived and the emergence of Dirac measures for
the respective filament tips is discussed.
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 two-dimensional systems.
Super-diffusive bounds for self-repelling 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
Landim-Quastel-Salmhofer-Yau (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 self-repelling
Large deviations for the two-dimensional two-component plasma
We derive a large deviations principle for the two-dimensional two-component 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.
Nonlinear diffusion: from particle models to gradient flows
This talk will study scale-bridging 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.
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 free, but compulsory for speakers and participants. Please follow the link: REGISTRATION PAGE
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: