About  Research  Events  People  Reports  Alumni  Contact  Home
89 January, 2013
YOUNG EUROPEAN PROBABILISTS 2013 (YEP X)
and
101112 January, 2013 SCHOOL on “Random Polymers” 
SUMMARY  REGISTRATION  SPEAKERS  PARTICIPANTS 
WORKSHOP:
The YEP workshop is the tenth in a successful series of meetings taking
place at Eurandom, Eindhoven. This year, the main focus of the workshop will be
on "random polymers".
A polymer is a large molecule consisting of monomers that are tied together by
chemical bonds. The monomers can be either small units (such as CH2 in
polyethylene) or larger units with an internal structure (such as the
adeninethymine and cytosineguanine base pairs in the DNA double helix).
Polymers abound in nature because of the multivalency of atoms like carbon,
oxygen, nitrogen and sulfur, which are capable of forming long concatenated
structures.
In the last years there has been a substantial progress in the understanding of
polymers from a mathematical point of view. Main tools for the analysis are
combinatorics, classical probability theory as well as the study of variational
formulas.
The workshop is filled by 15 invited young researchers who are at an early
stage of their career, and will give a talk about their own research topic.
there is also a minicourses, to provide an introduction to this area of
research by:
Alex Opoku  University of Leiden  Preparation for the course of F. Caravenna in the school 
SCHOOL:
The workshop will be immediately followed by a school on Random Polymers (Jan 101112).
The school consists of three mini courses by:
Francesco Caravenna  University of Milano  Probabilistic aspects of polymers 
Andrew Rechnitzer  University of British Columbia  Combinatorial aspects of polymers 
Stu Whittington  University of Toronto  General overview of polymers 
Besides the transfer of knowledge the workshop and the school aim at providing an inspiring
atmosphere to develop and deepen collaborative bonds with each other.
Former YEP
workshops
Registration is obligatory for all participants (organizers and speakers too!).
Please indicate on the registration form your attendance, participation in the lunches, dinner.
For minicourse and invited speakers, hotel accommodation will be
reserved. You are requested to indicate which nights you need accommodation on
the registration form.
Participants have to make their own hotelbooking. However, they can get a
reduced rate if they book our preferred hotel.
Please send an email to Patty Koorn for instructions on how to obtain this
special price.
For other bookings we suggest to consult the web pages of the
Tourist Information Eindhoven, Postbus 7, 5600 AA Eindhoven.
Dirk Erhard  Leiden University 
Nicolas Petrelis  Université de Nantes 
Nick Beaton  University of Melbourne  
Mathias Becker  WIAS Berlin  
Andrea Bedini  University of Melbourne  
Quentin Berger  USC Los Angeles  
Alessandra Cipriani  Universität Zurich  
Alexander Drewitz  Columbia University New York  
Gary Iliev  University of Toronto  
Gia Bao Nguyen  Université de Nantes  
Alex Opoku  Leiden University  
Marcel Ortgiese  TU Berlin  
Julien Poisat  University of Leiden  
Michele Salvi  TU Berlin  
Martin Slowik  TU Berlin  
Julien Sohier  Università Roma Tre  
Laurent Tournier  Université Paris 13  
Tilman Wolff  WIAS Berlin 
PROGRAMME YEP WORSKHOP
TUESDAY JANUARY 8
09.00  09.20  Registration + Coffee/tea  
09.20  09.30  Welcome  
09.30  11.00  Alex Opoku  Entropy, Relative Entropy and more 
11.00  11.30  BREAK  
11.30  12.00  Mathias Becker  SelfIntersection Local Times of Random Walks 
12.00  12.30  Tilman Wolff  Annealed asymptotics for occupation time measures of a random walk among random conductances 
12.30  14.30  LUNCH  
14.30  15.00  Quentin Berger  Influence of a correlated disorder in the polymer pinning model 
15.00  15.30  Gia Bao Nguyen  A variational formula for the free energy of a selfinteracting partially directed random walk 
15.30  15.45  BREAK  
15.45  16.15  Julien Sohier  
16.15  16.45  Julien Poisat  Random pinning model with weakly correlated environment 
16.45  17.00  BREAK  
17.00  17.30  Nick Beaton  Polymer adsorption on a rotated honeycomb lattice 
WEDNESDAY JANUARY 9
09.00  10.30  Alex Opoku  Entropy, Relative Entropy and more 
10.30  10.45  BREAK  
10.45  11.15  Alessandra Cipriani  Fluctuations near the limit shape of Young diagrams under a conservative measure 
11.15  11.45  Michele Salvi  Moment conditions for notzero speed of random walks among random conductances 
11.45  12.00  BREAK  
12.00  12.30  Andrea Bedini  
12.30  14.30  LUNCH  
14.30  15.00  Alexander Drewitz  
15.00  15.30  Marcel Ortgiese  Intermittency in branching random walks in random environment 
15.30  15.45  BREAK  
15.45  16.15  Laurent Tournier  Quenched and annealed fluctuations of random walks in random environment, in connection to dynamics of polymer phase transitions 
16.15  16.45  Martin Slowik 
Invariance principle for the random conductance model under moment conditions 
16.45  17.00  BREAK  
17.00  17.30  Gary Iliev 
PROGRAMME SCHOOL RANDOM POLYMERS
THURSDAY 1001
09.00  11.00  Stu Whittington  Polymer models and selfavoiding walks 
11.00  11.30  BREAK  
11.30  13.30  Andrew Rechnitzer  Enumerative combinatorics and models of polymers 
13.30  15.30  LUNCH  
15.30  17.30  Francesco Caravenna  
18.30   CONFERENCE DINNER 
FRIDAY 1101
09.00  11.00  Stu Whittington  Polymer models and selfavoiding walks 
11.00  11.30  BREAK  
11.30  13.30  Andrew Rechnitzer  Enumerative combinatorics and models of polymers 
13.30  15.30  LUNCH  
15.30  17.30  Francesco Caravenna  
SATURDAY 1201
10.00  11.00  Stu Whittington  Polymer models and selfavoiding walks 
11.00  11.15  BREAK  
11.15  12.15  Stu Whittington  Polymer models and selfavoiding walks 
12.15  13.15  Andrew Rechnitzer  Enumerative combinatorics and models of polymers 
13.15  14.00  LUNCH  
14.00  15.00  Andrew Rechnitzer  Enumerative combinatorics and models of polymers 
15.00  15.15  BREAK  
15.15  16.15  Francesco Caravenna  
16.15  16.30  BREAK  
16.30  17.30  Francesco Caravenna 
Nick Beaton
Polymer adsorption on a rotated honeycomb lattice
In a recent paper by BousquetMélou, de Gier, DuminilCopin, Guttmann and myself, it was proved that a model of selfavoiding walks on the honeycomb lattice, interacting with an impenetrable surface, undergoes an adsorption phase transition when the surface fugacity is $1+\sqrt{2}$.
Our proof used a generalisation of an identity obtained by DuminilCopin and Smirnov, and confirmed a conjecture of Batchelor and Yung. I consider a similar model of selfavoiding walk adsorption on the honeycomb lattice, but with the impenetrable surface placed at a right angle to the previous
orientation. For this model there also exists a conjecture for the critical surface fugacity, made in 1998 by Batchelor, BennettWood and Owczarek. I prove that this is indeed the critical fugacity. Many of the arguments used are very similar to those featured in the previous paper, but the new
orientation also introduces a number of subtle complications.
Mathias Becker
SelfIntersection Local Times of Random Walks
Consider a random walk on the lattice $\Z^d$ whose steps have mean zero and finite variance. For $p>1$, we study the number $\\ell_t\_p^p$ of $p$fold selfintersections up to time $t$. We derive the logarithmic asymptotics for $\P(\\ell_t\_p^p\geq r^p_t)$ for sequences $r^p_t$ in $(0,\infty)$, tending to infinity faster than $\E[\\ell_t\_p^p]$. The speed of the decay is identified in terms of mixed powers of $t$ and $r^p_t$, and the precise rate is characterized in terms of a variational formula. We will explain the appearance of two different regimes (sub and supercritical case) and thus the two different strategies of the random walk to produce the required amount of selfintersections.
Quentin Berger
Influence of a correlated disorder in the polymer pinning model
Abstract: In the study of critical phenomena, the question of the influence of disorder is central. The discussion is whether the presence of randomness changes or not the critical properties of the system. This question of relevance/irrelevance of disorder has recently been a great source of
investigation in the polymer pinning model, and is now mathematically understood in the case of an IID disorder. After introducing the pinning model and describing the existing results, we will comment on the influence of spatially correlated disorder in this framework. In particular, we will stress how very strong correlations can
have a crucial impact on the critical behavior of the system. In particular, we show that a "strong disorder" regime appears, where large fluctuations of disorder make it relevant.
Francesco Caravenna (mini course)
Probabilistic aspects of polymers
The aim of this course is to give an overview on some probabilistic models that describe the behavior of an inhomogeneous polymer chain interacting with an environment. A key feature of these models is that they undergo phase transitions: a slight variation of some external parameters, such as the temperature, can have a huge impact on the large scale properties of the polymer, producing interesting localization phenomena. We will mainly focus on two classes of models, called pinning and copolymer models, for which substantial progress has been obtained in recent years. From a mathematical viewpoint, these models may be described as inhomogeneous perturbations of the law of a random walk, depending on the realization of an additional source of randomness (disordered systems). Some of the challenging problems that arise will be analyzed in some depth, using a range of probabilistic techniques.
Alessandra Cipriani Fluctuations near the limit shape of Young diagrams under a conservative measure In this work we are considering the behavior of the limit shape of Young diagrams associated to random permutations on the set {1,...,n} under a particular class of multiplicative measures. Our method is based on generating functions and complex analysis (saddle point method). We show that fluctuations near a point behave like a normal random variable and that the joint fluctuations at different points of the limiting shape have an unexpected dependence structure. We will also give further directions of research concerned with the randomization of the cycle counts of permutations and on the convergence to a continuous stochastic process. This is a joint work with Dirk Zeindler.
Alex Drewitz
Effective polynomial ballisticity conditions for random walk in random environment
The conditions $(T)_\gamma,$ $\gamma \in (0,1),$ which
have been introduced by Sznitman in 2002, have had a significant impact on
research in random walk in random environment. They require the stretched
exponential decay of certain slab exit probabilities for the random walk under
the averaged measure and are asymptotic in nature. We show that in all relevant
dimensions (i.e., $d \ge 2$), in order to establish the conditions $(T)_\gamma$,
it is actually enough to check a corresponding condition $(\mathcal{P})$ of
polynomial type on a finite box. In particular, this extends the
conjectured equivalence of the conditions $(T)_\gamma,$ $\gamma \in (0,1),$ to
all relevant dimensions.
(joint work with N. Berger and A.F. Ramírez)
Gia Bao Nguyen
A variational formula for the free energy of a selfinteracting partially directed random walk
Long linear polymers in dilute solutions are believed to undergo a collapse transition from a random coil (expand itself) to a compact ball (fold itself up) when the temperature is lowered, or the solvent quality deteriorates. A natural model for this phenomenon is a $1+1$ dimensional selfinteracting and partially directed selfavoiding walk. In this paper,
we develop a new method to study the partition function of this model, from which we derive a variational formula for the free energy. This variational formula allows us to prove the existence of the collapse transition and to identify the critical temperature in a simple way. We also prove that the order of the collapse transition is $3/2$.
Alex Opoku
Entropy, Relative Entropy and more The notions of entropy, relative entropy and their densities will be reviewed in this course. We will exhibit : • some of their key properties. • how they are used in obtaining bounds on probabilities, in particular how they naturally appear in large deviation theory as rate functions. This course serves as a preparation for the course that will be given by F. Caravenna later at the school.
Marcel Ortgiese
Intermittency in branching random walks in random environment
We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. (timeindependent) potential. When keeping the potential fixed, the averaged number of particles satisfies the heat equation with a random potential known as the parabolic Anderson model. In the last twenty years, there has been
considerable progress in understanding the longterm behaviour of the averaged system. We concentrate on the situation when the potential is Paretodistributed and we will discuss the effect of the averaging. In particular, we will see that even though the qualitative picture is the same, the nonaveraged system does not localize in the sites that are predicted
by the heat equation. (joint work with Matt Roberts)
Julien Poisat
Random pinning model with weakly correlated environment
The random pinning model is a model of Statistical Mechanics dealing with the (de)localization transition of a polymer interacting with an interface or with another polymer, via a disordered potential. The example of DNA denaturation is a motivation for studying the effect of correlations in the disorder sequence on the model. The purpose of this
talk is to give some results for weak correlations: in this regime, even if some quantities associated to the model are modified (such as critical point shifts), some qualitative features (such as the annealed critical exponent) are proved to remain unchanged. I will explain how one can
connect the decay of correlations with the regularity of some potential function, and how one can then use the spectral properties of an appropriate RuellePerronFrobenius operator to derive these results.
Andrew Rechnitzer (mini course)
Enumerative combinatorics and models of polymers
Many problems in mathematics and physics  including
many in the modeling of polymers  can be rephrased as "How many...".
Enumerative combinatorics seeks to answer these questions. Over the course of 2
or 3 lectures I will give a general introduction to the world of enumeration and
the techniques of generating functions  including asymptotic methods championed
by the late Philippe Flajolet.
In the second half of the short course I will show how we can apply these
generating function methods to study polymers  especially adsorption, collapse
and localisation.
Michele Salvi
Moment conditions for notzero speed of random walks among random conductances
Reversible random walks in random environment are called random walks among random conductances. It is well known that whenever one considers weights on the edges of the euclidean lattice (the conductances) bounded from above, the corresponding process has almost surely zero
limiting speed. We derive sharp logmoments conditions on the distribution of the conductances that force the random walk to have zero speed. We also show counterexamples relying on geometrical constructions of random trees of walks with positive speed, or even notexisting speed, whenever such conditions are not
fulfilled. (joint work with Noam Berger, TU Munich)
Martin Slowik
Invariance principle for the random conductance model under moment conditions
We consider a continuous time random walk on the lattice
$\mathbb{Z}^d$ in an environment of random conductances, $\mu_{x,y}$. The law of
the environment is assumed to be ergodic with respect to space shifts with $\mathbb{P}[0
< \mu_{x,y} < \infty] = 1$. In this talk, I will explain how a quenched
invariance principle can be established under suitable moment conditions. A key
ingredient in the proof is to establish the sublinearity of the corrector by
means of Moser's iteration scheme.
(joint work with Sebastian Andres (Univ. Bonn) and JeanDominique Deuschel (TU
Berlin)).
Laurent Tournier
Quenched and annealed fluctuations of random walks in random environment, in connection to dynamics of polymer phase transitions
In this talk, we will present how some problems about random walks in onedimensional random environment (RWRE) arose in the physics litterature in the context of phase transition in random polymers (here, random polymers refer to chains of randomly chosen monomers, like DNA,
rather than random spatial configurations of a chain), and present recent results that provide a rigorous setting and new developments. We will be led to focus at the quenched distribution of the hitting times of an RWRE, as a quenched counterpart to a celebrated result by Kesten, Kozlov and Spitzer. This is a joint work with N. Enriquez, C. Sabot and O. Zindy.
Stu Whittington (mini course)
Polymer models and selfavoiding walks
The lectures will give an introduction to polymers and to some lattice models used to investigate their conformational properties. After a brief introduction to some classes of polymers and the kinds of questions that one would like to address, most of the time will be spent on selfavoiding walks. Some useful general techniques will be introduced in cluding subadditive inequalities, unfolding operations and pattern theorems. Applications will include models of polymer adsorption, polymers in confined geometries and random knotting.
Tilman Wolff
Annealed asymptotics for occupation time measures of a random walk among random conductances
The annealed asymptotic behaviour of local times, or occupation time meaasures, of a simple random walk is key to the longtime analysis of the solution to the parabolic Anderson problem, that is, the heat equation on the lattice with random potential.
Dependent on the tails of the potential distribution, it is crucial to establish large deviation principles for properly rescaled local times on fixed or timedependent domains. The random conductance model (RCM) describes a random walk with locally irregular diffusive dynamics, which seems in many cases more realistic than the homogeneous random walk. With a view to future analysis of the parabolic Anderson model with random conductances, it makes sense to
study the occupation time measures of a random walk among random conductances in terms of large deviation principles. We work in the case of conductances that assume arbitrarily small values with exponentially small probability. Here, the scale of the corresponding large deviation principles is different from the SRW case.
We will focus on timedependent domains and also address dimensiondependent properties of the correponding continuous variational problems.
Name  Firstname  Affiliation 
Beaton

Nicolas  Université Paris 13 

Mathias  WIAS Berlin 
Bedini  Andrea  University of Melbourne 
Berger  Quentin  University of Southern California 
Birkner  Matthias  University of Mainz 
Caravenna  Francesco  University of Milano 
Cheliotis  Dimitris  University of Athens 
Cipriani  Alessandra  University of Zurich 
den Hollander  Frank  Leiden University 
Drewitz  Alexander  Columbia University 
Erhard  Dirk  University of Leiden 
Fitzner  Robert  TU Eindhoven / Eurandom 
Iliev  Gerasim  York University 
Klimovsky  Anton  Leiden University 
Komjathy  Julia  TU Eindhoven 
Lacoin  Hubert  Paris (Université Paris Dauphine) 
Mortimer  Paul  Queen Mary University of London 
Nardi  Francesca  TU Eindhoven 
Nguyen  Gia Bao  Université de Nantes 
Opoku  Alexander  Leiden University 
Ortgiese  Marcel  TU Berlin 
Osborn  JudyAnne  Univeristy of Newcastle 
Pétrélis  Nicolas  Université de Nantes 
Poisat  Julien  University of Leiden 
Rechnitzer  Andrew  University of British Columbia 
Salvi  Michele  TU Berlin 
Schwerdtfeger  Uwe  Technishce Universität Chemitz 
Slowik  Martin  TU Berlin 
Sohier  Julien  Università degli studi di Roma Tre 
Stodtmann  Sven  University of Heidelberg 
Sun  Rongfeng  National University of Singapore 
Tournier  Laurent  Université Paris XIII 
van der Hofstad  Remco  TU Eindhoven / Eurandom 
Whittington  Stu  University of Toronto 
Wolff  Tilman  WIAS Berlin 
Conference Location
The workshop location is Eurandom, Den Dolech 2, 5612 AZ
Eindhoven, METAFORUM, 4th floor, MF 12.
Eurandom is located on the campus of Eindhoven University of Technology, in the 'Laplacegebouw' building' (LG on the map). The university is located at 10 minutes walking distance from Eindhoven railway station (take the exit north side and walk towards the tall building on the right with the sign TU/e).
For all information on how to come to Eindhoven, please check http://www.eurandom.tue.nl/contact.htm
CONTACT
For more information please contact
Mrs. Patty Koorn,
Coordinator of
EURANDOM
OTHER SPONSORS

Last updated
010713,
by
PK