Thursday, April 1

09:00-10:30 Eric Presutti
10:00-10:30 coffee/tea break
10:30-11:30 Dima Ioffe: "Semi-directed polymers in random environment"
11:30-11:40 Short Break
11:40-12:20 Dmitris Cheliotis: "Disorder relevance for pinned random polymers"
12:20-14:30 lunch break
14:30-15:10 Alessandra Bianchi
15:10-15:50 Patric Gloede: "Martingale problems for tree-valued branching processes"
15:50-16:20 Coffee break
16:20-17:00 Sven Piotrowiak: "Marked metric measure spaces: A suitable state
17:00-17:40 Anita Winter
19:00 - Conference Dinner

 

Saturday, April 3

09:00-10:30 Damien Simon "Branching random walks : selection, survival and genealogies"
10:00-10:30 coffee/tea break
10:30-11:30 Andrej Depperschmidt: "Modelling Protein Translocation: A Brownian Ratchet"
11:30-11:40 Short Break
11:40-12:20 Peter Pfaffelhuber: "Bacterial population genomics"
12:20-14:30 lunch break

 

Andrej Depperschmidt: "Modelling Protein Translocation: A Brownian Ratchet"
 Motivated by protein translocation models we consider a Brownian ratchet. It is defined as a reflecting Brownian motion B_t with moving reflection boundary given by a non-decreasing jump process R_t. At rate proportional to B_t - R_t a new boundary is chosen uniformly in the interval [R_t;B_t]. In the talk we outline the proof of the law of large numbers and the central limit theorem for the Brownian ratchet.

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Dmitris Cheliotis: "Disorder relevance for pinned random polymers"
We consider a directed random polymer interacting with an interface that carries random charges some of which attract while others repel the polymer. Such a polymer is known to exhibit a localized or delocalized phase depending on the temperature and the average bias of the disorder. At a given temperature, there is a critical bias separating the two phases. A question of particular interest, and which has been studied extensively, is whether the quenched critical bias differs from the annealed critical bias. When it does, we say that the disorder is relevant. We present a necessary and sufficient condition for relevance that gives easily some known results as well as new ones. The essential tool in our approach is a quenched Large Deviations Principle proved recently by Birkner, Greven, and den Hollander. This is joint work with F. den Hollander.

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Alessandra Bianchi: "Coupling in potential wells: from average to pointwise estimates of metastable times"
In many situations of interest, the potential theoretic approach tometastability allows to derive sharp estimates for quantities characterizing the metastable behavior of a given system. In this framework, the average metastable times can be expressed through the capacity of corresponding metastable sets, and capacities can be estimated with the application of two different variational principles, providing upper and lower bounds. After recalling these basic concepts and techniques, I will describe a new method to couple the dynamics inside potentials wells. Under some general hypothesis, I will show that this yields sharp estimates on metastable times, pointwise on any metastable set. Our key example will the random field Curie-Weiss model.

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Alex Gaudilliere: "An upper bound for front propagation velocities inside moving populations"
We consider a two-kind particle population(red and blue, or R and B) that evolves on the lattice according to a reaction-diffusion process R+B -> 2R starting from a single red particle in the midst of a density of blue particles. We modelize in this way the propagation of an information or an epidemy inside a moving population, or the progression of a combustion front. We give, in function of the population density, an upper bound for the propagation velocity, that holds in many different situations: the diffusion constant of the red an blue particles can be identical or different, we can also consider, in a low density regime, dynamics with exclusion and attraction. This allows in particular a control of long range correlations during the evolution of an interracting particles system.

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Patric Gloede: "Martingale problems for tree-valued branching processes"
We consider a stochastic process describing the evolution of the genealogy of a branching process which depends quadratically on the population size. This is a piecewise deterministic Markov process and its martingale problem can be characterized precisely. Rescaling the process gives a tree-valued geometric Brownian motion exhibiting an interesting connection with the tree-valued Fleming- Viot process.

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Martin Hutzenthaler: "Excursions of some one-dimensional diffusions"
A Brownian path from time zero to time t can be viewed as concatenation of excursions from zero plus a last piece. Such last exit decompositions exist for general regular one-dimensional diffusions. Recall that a point is regular if it is accessible but not absorbing. Excursions from an absorbing point are slightly different. We show how path decompositions, e.g. the Williams decomposition, provide us with formulas for the excursion measure of an absorbing point. Now consider a diffusion on the nonnegative reals for which zero is absorbing and add immigration of mass at rate epsilon. Then zero is a regular point. As epsilon tends to zero the last exit decomposition - suitably rescaled - converges to a non-trivial limit which involves the excursion measure of the diffusion without immigration.

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Dima Ioffe: "Semi-directed polymers in random environment"
We describe recent results with Yvan Velenik on geometry and fluctuations of stretched polymers in annealed and (weak) quenched disorder.

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Nabin Jana: "Random Energy Models in the light of LDP"
Use of large deviation principle to analyze the free energy of the Gaussian random energy model is gone back to 2000, thanks to Dorlas and Wedagedera. We highlight the method how it can be used to analyze several other random energy models with external fields and present some cute observations.

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Nicola Kistler: "Non-linear transformations of the Generalized Random Energy Model"
I will introduce a version of Derrida's Generalized Random Energy Model (GREM) which, contrary to the original GREM, lacks a certain linearity in the hamiltonian. The model shows a most curious behavior: it performs 'minimum' likelihood estimation to identify certain random temperatures which are, in turn, at the heart of the convergence of the extremal process towards the socalled Derrida-Ruelle cascades.

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Anton Klimovsky: "Parisi landscapes in high-dimensional Euclidean spaces"
Recently, Bouchaud and Fyodorov have introduced and analysed a model of random landscapes in high-dimensional Euclidean spaces. This model is based on stationary and rotationally invariant Gaussian randompotentials. The original analysis is based on the celebrated but mathematically unjustified replica symmetry breaking Ansatz due to Parisi. We report on our rigorous analysis of this model.

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Christian Maes: "On the response of nonequilibria to external stimuli"
We unify a number of recent proposals dealing with extensions andmodifications of the fluctuation-dissipation theorem to nonequilibrium systems. Our nonequilibrium fluctuation-dissipation relation (FDR) includes a dynamical correlation between the observable and the excessin activity caused by the applied extra potential, where activity is an expression of time-symmetric traffic between the states of the system. We also discuss how the additive correction to FDR can become a multiplicative correction as embodied in the concept of effective temperature for long-lived transients of detailed balance dynamics. Joint work with Marco Baiesi and Bram Wynants.

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Peter Pfaffelhuber: "Bacterial population genomics"
The genome of bacteria is less stable than the genome of eucariotes. In particular, it is an empirical observation that bacteria from the same population carry different genes. We study a model where new genes are introduced from the environment and can be lost along ancestral lines. By randomizing the genealogy according to a Kingman coalescent this mutation model, which appears to be new in the population genetic literature, can be analyzed. Moreover, empirical data fit well with our theoretical results. This is joint work with Franz Baumdicker, Wolfgang Hess, University of Freiburg.

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Sven Piotrowiak: "Marked metric measure spaces: A suitable state space for treevalued Ohta-Kimura resampling dynamics"
In contrast to the Moran model the resampling rates of the Ohta-Kimura model depend on the types of the individuals. In order to describe the genealogies of such models and of their diffusion limits we want to introduce a suitable state space for such processes: the space of marked metric measure spaces. Equipped with an appropriate topology this space becomes Polish.

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Damien Simon "Branching random walks : selection, survival and genealogies"
Branching random walks are one of the simplest physics models that have many applications in evolutionary biology and ecology. This talk will be an overview of the results obtained on this branching walks. More precisely, I will consider the effect of absorbing boundaries (predators,pollution) on the survival of a population of branching random walk and study the phase transition to the absorbing state. In a second part, I will present the point of view of the genealogies to characterize the different types of selection. Links will be made with other problems of statistical mechanics such as directed polymers in random media.

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