Marc Mézard

Laboratoire de Physique Théorique et Modeles Statistiques
Batiment 100, Université de Paris Sud
91405 Orsay - France

E-mail: (Mon nom de famille, i.e. my last name) "at"
Bureau: 202
Téléphone: +33 (0)1 69 15 73 33
Fax: +33 (0)1 69 15 65 25
How to get to Orsay?

Depuis avril 2012, je suis devenu directeur de l'Ecole normale supérieure. La présente page concerne mes activités de recherche, pour en savoir plus sur mes activités à l'ENS vous pouvez consulter :




My general interest is the statistical physics of disordered systems. A system can be disordered either because each particle (or spin, or neuron, or economic agent...) is different from all other ones, or because it sees a different environment: generally this happens in a glassy phase, in which the various particles freeze in some positions which look random, and don't have the periodicity of a crystal. In these cases it turns out to be very difficult to even understand the basics of the collective behaviour, such as the phase diagram. This field has been one of the main developments of statistical physics in the last two or three decades. In classical physics, it basically started with spin glasses, and some offsprings developed gradually towards such diverse systems as combinatorial optimization problems, error correcting codes, neural networks, structural glasses, or systems of interacting economic agents with heteronegeous strategies. The paper

which I have prepared for a book in honour of Sam Edwards (A volume pub;lished by Oxford Science Publications, entitled "Stealing the gold", edited by Paul M. Goldbart, Nigel Goldenfeld and David Sherrington, in which you can find many interesting contributions), gives some general and non technical background to the evolution of this field.
The link brings you to a recent short 'perspective' article which I wrote for Science on the efficiency of message passing procedures in optimization, physics, and information theory.
This other perspective points to a recent application of message passing to data clustering by finding exemplars:
L' article écrit pour la 'Lettre de l'academie des Sciences', fournit une très brève introduction en francais.

The book that we have written together with Andrea Montanari is now available from all good bookshops, or directly on the website of Oxford University Press:

All comments are very welcome!

The book with Parisi and Virasoro on "Spin glass theory and beyond" explains the mean field theory of spin glasses and some of its early applications to problems in optimization and neural networks. It was published in 1987 by World Scientific, see: "Spin glass theory and beyond" .

Statistical physics and combinatorial opimization
In the last few years I was involved a lot in some research program about combinatorial optimization. Recently we succeeded in finding the phase diagram of the K=3 satisfiability problem; these analytic developments also allow to introduce a completely new type of optimization algorithms which looks quite powerful. See:
Our algorithm of "Survey Propagation" for solving random SAT problems of large size, together with some documentation, is available here:
Structural glasses
I have a long lasting interest in the Statistical Physics of structural glasses. Here is a review paper on this topic: