INHOMOGENEOUS RANDOM SYSTEMS
Tuesday 24 and Wednesday 25 January 2012 Schedule
The aim of this annual workshop, in conjunction with the "Rencontres de Physique Statistique", is to bring together mathematicians and physicists working on disordered or random systems, and to discuss recent developments on themes of common interest. Each of the two days is devoted to a specific topic:
Tuesday 24 January: Quasi stationary distributions and Fleming Viot processes.
Moderator: Pablo Ferrari (Buenos Aires)
Quasi stationary distributions appear as the limiting distribution of an absorbing Markov process conditioned to non absorption. In contrast with usual (non absorbing) irreducible Markov processes which accept at most one invariant measure, there may be infinitely many qsd for countable state absorbing Markov chains. The Fleming Viot process is a particle system of N particles moving independently with the transition rates of the absorbing Markov chain but when a particle is absorbed, it chooses randomly one of the other particles and jumps to its site. There are several works giving conditions for the following results. The empirical distribution of the Fleming Viot process converges to the motion of the absorbing Markov chain conditioned to non absorption. The empirical distribution of the invariant measure of the FV process converges to a qsd. There are other ways to approach the qsd using the empirical cumulated distribution and some supercritical branching processes. Experts in these themes will participate in this meeting.
Speakers: Amine Asselah (Créteil), Nathanaël Berestycki (Cambridge), Alexandre Gaudillière (Marseille), Ilie Grigorescu (Miami), Pablo Groisman (Buenos Aires), Claude Le Bris (Marne la Vallée), Denis Villemonais (Palaiseau).
Titles and abstracts
Wednesday 25 January: Lifson-Poland-Scheraga models of DNA.
Moderator: Roberto Livi (Firenze)
Since the discovery of the helicoidal structure of DNA,
the phenomenon of its transformation to a coil under
heating has been tackled as an equilibrium phase transition.
Basic works by Lifson and subsequently by Poland
and Scheraga [1, 2] led to a model that is still today the
object of investigation. This one-dimensional model is
known to exhibit a phase transition because of the existence
of long-range interactions. Recently, some authors
have proposed a new mechanism ruling DNA denaturation
as an abrupt first-order phase transition [3, 4],
at variance with the previous theoretical considerations
in favor of a continuous one. On the experimental side
the situation is still far from conclusive.
Previous measurements indicated the presence of a sharp jump in the
fraction of bound base pairs [5, 6]. More recently, the
results reported in  have been interpreted as an indication
of a weakly continuous phase transition. More
recently some authors have concluded on rigorous mathematical
basis  that the denaturation transition turns
to a continus one in the presence of quenched disorder,
in contrast with results obtained by numerical investigations .
Moreover, little is known about the dynamics
of this denaturation transition. We can mention the contributions
based on a mechanical approach [10, 11] and
on a Langevin description of the two DNA-strands as
polymers in continuous space . More recently, this
problem has been reconsidered and analyzed by analytic
and numerical studies, e.g. see [13, 14].
Accordingly, a meeting making the point about such basic questions and presenting recent achievements on the LPS-model is timely and appropriate. References.
Speakers: Marco Baiesi (Padova), Giambattista Giacomin (Paris), Yariv Kafri (Haifa), Hervé Kunz (Lausanne), David Mukamel (Rehovot), Julien Poisat (Lyon).
Titles and abstracts
|François Dunlop||Thierry Gobron||Ellen Saada|
|Physique Théorique et Modélisation||Physique Théorique et Modélisation||Mathématiques Appliquées|
|Université de Cergy-Pontoise||Université de Cergy-Pontoise||Université Paris Descartes|
|(33)1 3425 7509||(33)1 3425 7511||(33)1 4286 2114|