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January 14 - 18, 2013 Workshop on Random Polymers
The theme of the workshop is random polymers in the
broad sense of the word. Targeted are not only researchers from probability
theory, but also from combinatorics, physics and physical chemistry. Polymers
with disorder are part of the workshop, but are not the main focus.
REGISTRATION There is no deadline for registration, but the number of places is limited. For organizational reasons registration is obligatory for all participants (organizers and speakers included). Please indicate on the registration form your attendance, participation in the lunches, dinner. For invited speakers hotel accommodation will be arranged
by the organization. You are requested to indicate the arrival and departure
dates on the registration form.
Monday Jan 14
Tuesday Jan 15
Wednesday Jan 16
Thursday Jan 17
Friday Jan 18
Ken Alexander Path properties of the random pinning polymer in the delocalized regime We study the path properties of the random pinning model
in the delocalized regime and we prove that, at any temperature, the likely
number of contacts with the defect line under the (random) Gibbs measure stays
bounded in probability as the polymer length grows. On the other hand we also
show that at sufficiently low temperature, there exists a.s. a subsequence where
the likely number of contacts grows like the log of the length of the polymer. Matthias Birkner Quenched large deviations for continuous words and an application to the Brownian copolymer
We describe the quenched large deviation rate function for the empirical
processes obtained by cutting a Brownian path along a continuous-time renewal
process, and discuss how this can be employed to study a continuous copolymer
model. Mireille Bousquet-Mélou The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is 1+\sqrt 2 In 2010, Duminil-Copin and Smirnov proved a
long-standing conjecture of Nienhuis, made in 1982, that the growth constant of
self-avoiding walks on the hexagonal lattice is \mu=\sqrt{2+\sqrt 2}. A key
identity used in that proof was later generalised by Smirnov so as to apply to a
general O(n) loop model with n in [-2,2] (the case n=0 corresponding to SAWs).
We modify this model by restricting to a half-plane and introducing a fugacity
associated with boundary sites (also called surface sites) and obtain a
generalisation of Smirnov's identity. The value of the critical surface fugacity
was conjectured by Batchelor and Yung in 1995. This value also plays a crucial
role in our identity, which thus provides an independent prediction for it. For
the case n=0, corresponding to SAWs interacting with a surface, we prove the
conjectured value of the critical surface fugacity. A critical part of this
proof involves demonstrating that the generating function of self-avoiding
bridges of height T, taken at its critical point 1/\mu, tends to 0 as T
increases, as predicted from SLE theory. Richard Brak Polymers, Particle Hopping and a change in basis This talk will discuss the connection between an equilibrium polymer phase transition and the non-equilibrium phase transition in a particle hopping model and how this connection arouse out of studying the combinatorics of the change in vector space basis of ASEP algebra representations. Philippe Carmona Phase transition for the partially directed polymer A long linear polymer in a dilute solution is modelled by a partially directed self avoiding random walk with self-interactions. We prove the existence of a collapse transition, identify the critical temperature, and establish that the order of the transition is 3/2 Xia Chen Exponential asymptotics for time-space Hamiltonians Dimitris Cheliotis On the quenched critical curve of the random pinning model We improve a recent formula for the quenched critical curve of the random pinning model, and show some of its applications. Francis Comets Mean-field Last Passage Percolation We consider a system of N particles with a stochastic
dynamics introduced by Brunet and Derrida. The particles can be interpreted as
last passage times in directed percolation on {1,...,N} of mean-field type. The
particles remain grouped and move like a traveling wave, subject to
discretization and driven by a random noise. As N increases, we obtain estimates
for the speed of the front and its profile, for different laws of the driving
noise. The Gumbel distribution plays a central role for the particle jumps, and
we show that the scaling limit is a Levy process in this case. The case of
bounded jumps yields a completely different behavior. Ivan Corwin A rigorous replica trick for directed polymers We develop a rigorous replica trick for certain integrable
deformations of the directed polymer model. Under the limit which recovers the
polymer, the rigorous approach degenerates to the physicists famously
non-rigorous manipulations. ASEP and q-TASEP both work as deformations and
inspiration from the theory of Macdonald processes serves as the key to the
computations. Sacha Friedl Chains with complete connections and modified majority rules We take a closer look at a type of chains with complete
connections introduced by Berger, Hoffman and Sidoravicius [BHS]. In that model,
the distribution of the present when conditioned on the whole past is determined
by the majority rule, looking at the values of the process on a random finite
subset of the past. Giambattista Giacomin Oscillatory critical amplitudes and near-constancy phenomena The talk focuses on hierarchical pinning models, that is pinning models on diamond lattices, and aims at analyzing the critical behavior. An unexpected phenomenon takes place: the critical behavior is not 'pure power law', in the sense that the power law has a prefactor - the amplitude - which is not constant, but periodic. The aim of the talk is in particular to show the tight link with an analogous phenomenon observed for Galton-Watson trees by T. E. Harris (and in several other branches of mathematics after that) and to explain why this oscillation is directly linked to the geometry of the Julia set of the map that defines the diamond lattice (or the Galton-Watson tree): this link had been conjectured by Derrida, Itzykson and Luck in 1984. Other recent results will be reported. Tony Guttmann Off-critical parafermions and the winding angle distribution of SAWs Using an off -critical deformation of the identity of Duminil-Copin and Smirnov, we prove a relationship between half-plane surface critical exponents and wedge critical exponents with the exponent characterising the winding angle distribution of the SAW model in the half-plane, or more generally in a wedge. We assume only the existence of these exponents. If we assume their values as predicted by conformal field theory, one gets complete agreement with the conjectured winding angle distribution, as obtained by CFT and Coulomb gas arguments. Gary Iliev Pattern recognition in polymeric systems: modeling copolymers near an inhomogeneous surface We present partially-directed and self-avoiding walk
models of copolymers interacting with an inhomogeneous surface, in the absence
and presence of an elongational force. In all cases, we observe qualitative
agreement between the results obtained via the directed walk model and those
from self-avoiding walks. When the polymer is subject to an elongational force,
we also use a simple low temperature treatment to understand the behaviour of
both models. We solve the directed walk problem essentially completely and
study the force-temeprature phase diagram in various regimes of the direction
and strength of the applied force. Dima Ioffe Interaction, repulsion and scaling of low temperature interfaces I shall describe recent results on interaction and
entropic repulsion between low temperature Ising type interfaces (which, given
the circumstances, will be called Ising polymers) in two dimensions. Hubert Lacoin Counting self-avoiding paths on an infinite supercritical percolation cluster The self-avoiding walk on $\mathbb{Z}^d$ has been introduced by
Flory and Ott as a natural model for polymers. Fabio Martinelli Dynamics of 2 + 1 dimensional sos surfaces above a wall: slow mixing induced by entropic repulsion We study the Glauber dynamics for the (2+1)d Solid-On-Solid
model above a hard wall and below a far away ceiling, on an LxL box of Z^2 with
zero boundary conditions, at large inverse-temperature β. Alex Opoku Copolymer with Pinning: A view from a variational window In a recent paper, Dimitris Cheliotis and Frank den
Hollander have developed a variational approach to the study of the random
pinning model, based on a large deviation principle for random words drown from
random letters by M. Birkner, A. Greven and F. den Hollander. Aleks Owczarek Exact solution of two friendly walks above a sticky wall with single and double interactions We find, and analyse, the exact solution of two friendly directed walks, modelling polymers, which interact with a wall via contact interactions. We specifically consider two walks that begin and end together so as to imitate a polygon. We examine a general model in which a separate interaction parameter is assigned to configurations where both polymers touch the wall simultaneously, and investigate the effect this parameter has on the integrability of the problem. We find an exact solution of the generating function of the model, and provide a full analysis of the phase diagram that admits three phases with one first-order and two second-order transition lines between these phases. Nicolas P étrélisPhase diagram of a copolymer in an emulsion In this talk we consider a model for a random copolymer,
made of monomers of type A and B, immersed in a micro-emulsion of random
droplets of type A and B. The emulsion is modeled by large square blocks filled
randomly with solvents A and B and the possible configurations of the copolymer
are given by the trajectories of a partially directed random walk in dimension
2. The copolymer and the emulsion interact via an Hamiltonian which favors
matches and disfavors mismatches. Thomas Prellberg The pressure of surface-attached polymers and vesicles A polymer grafted to a surface exerts pressure on the substrate.
Similarly, a surface-attached vesicle exerts pressure on the substrate. Buks van Rensburg Some results on inhomogeneous percolation Chris Soteros Knot transition probabilities and knot reduction for lattice strand passage models of ring polymers
Rongfeng Sun Symmetric Rearrangements Around Infinity with Applications to Levy Processes We prove a new rearrangement inequality
for multiple integrals, which partly generalizes a result of Friedberg and
Luttinger and can be interpreted as involving symmetric rearrangements of
domains around infinity. As applications, we prove two comparison results for
general Levy processes and their symmetric rearrangements. The first application
concerns the survival probability of a point particle in a Poisson field of
moving traps following independent Levy motions. We show that the survival
probability can only increase if the point particle does not move, and the traps
and the Levy motions are symmetrically rearranged. This essentially generalizes
an isoperimetric inequality of Peres and Sousi for the Wiener sausage. In the
second application, we show that the q-capacity of a Borel measurable set for a
Levy process can only increase if the set and the Levy process are symmetrically
rearranged. This result generalizes an inequality obtained by Watanabe for
symmetric Levy processes. Fabio Toninelli L^{1/3} fluctuations for the contours of the 2D SOS model We consider the two-dimensional discrete SOS model at
low temperature T in a LxL box. In presence of a wall at height zero, the
surface is tipically at height (T/4)log(L) (due to entropic repulsion). We show
that the level lines of the interface, once rescaled by 1/L, have a
deterministic limit described by a suitable Wulff shape, and that the
fluctuations around the limit shape are of order L^{1/3} (before rescaling).
This seems to be connected with the "1/3-type fluctuations" one finds in growth
models and directed polymers in (1+1) dimensions. Carlo Vanderzande Fractional Brownian motion and the critical dynamics of zipping polymers We consider two complementary polymer strands of length
L attached by a common end monomer. The two strands bind through complementary
monomers and at low temperatures form a double stranded conformation (zipping),
while at high temperature they dissociate (unzipping). Nobuo Yoshida Brownian Directed Polymers in Random Environment: Complete Localization and Phase Diagram This is a joint work with Francis Comets. We study a model of directed polymers in random environment in dimension $1+d$, givenby a Brownian motion in a Poissonian potential. We study the effect of the density and the strength of inhomogeneities, respectively the intensity parameter $\nu$ of the Poisson field and the temperature inverse $\beta$. Our results are: (i) fine information on the phase diagram, with quantitative estimates on the critical curve; (ii) pathwise localization at low temperature and/or large density; (iii) complete localization in a favourite corridor for large $\nu \beta^2$ and bounded $\beta$. Nicolas Zygouras Geometric RSK, Whittaker Functions and Random Polymers (with or without pinning) Whittaker functions are special functions, which have a
central position in representation theory and integrable systems. Surprisingly,
they turn out to play a central role in the fluctuation analysis of Random
Polymer Models. In this talk I will explain the emergence of Whittaker functions
in Random Polymer Models, via the use of Geometric Robinson-Schensted-Knuth
correspondence (RSK). I will then describe their role in the computation of the
distribution of partition functions, where also a certain pinning may be
allowed.
Conference Location
For all information on how to come to Eindhoven, please check http://www.eurandom.tue.nl/contact.htm
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Last updated
25-04-13,
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