INHOMOGENEOUS RANDOM SYSTEMS Tuesday 24 and Wednesday 25 January 2012 Schedule Institut Henri Poincaré 11, rue Pierre et Marie Curie Paris

SHEPI

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 [7] have been interpreted as an indication of a weakly continuous phase transition. More recently some authors have concluded on rigorous mathematical basis [8] that the denaturation transition turns to a continus one in the presence of quenched disorder, in contrast with results obtained by numerical investigations [9]. 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 [12]. 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 The conference is free and open to all.