Raphaël CERF

Mathématiques,
Université Paris-Saclay,
91405 Orsay Cedex,           
France

Courrier électronique :
Use the standard address of the maths department.
 
Currently working at ENS, Paris.
Photo 


I have written simulation programs for the Ising model and for bond and site percolation, in C++ under Linux. I have developed a graphical interface on the Mac.
These programs use the Gnu Scientific Library and they are available on demand.
Below you see, from left to right, a critical Ising model, a critical percolation configuration, clusters meeting a ball and a Wulff Ising droplet.

      
Critical Ising
              model    Critical percolation    Clusters crossing a ring    Wulff Ising droplet

By clicking on an image, you will see further samples of the same types. Here are some simulations witnessing the phase transition in the Ising model and in percolation. Please help yourself!


I had the pleasure to supervise the following PhD thesis:

Olivier Couronné, Sur les grands clusters en percolation

Reda Messikh, Du modèle d'Ising 2D vers un problème de Mumford–Shah à deux couleurs

Alexandre Gaudillère (the true director is Enzo Olivieri), Fuga dalla metastabilità per dinamiche stocastiche conservative

Marie Théret, Grandes déviations pour le flux maximal en percolation de premier passage

Pierre Petit, Sur la théorie de Cramér et sa généralisation aux champs asymptotiquement découplés

Matthias Gorny, Un modèle d'Ising Curie-Weiss de criticalité auto-organisée

Joseba Dalmau, La quasi-espèce pour une population finie

Wei Zhou, Un nouveau regard sur les interfaces dans les modèles de percolation et d'Ising

Nicolas Forien, Autour de la criticité auto-organisée

Maxime Berger, Le comportement critique de la quasi-espèce

I love to cooperate with other mathematicians and I have written papers with (in alphabetical order):
Laurent Alonso, Gérard Ben Arous, Nathanaël Berestycki, Maxime Berger, Stefano Bianchini, Olivier Catoni, Emilio Cirillo,
Paolo Dai Pra, Joseba Dalmau, Barbara Dembin, Nicolas Forien, Marco Formentin, Matthias Gorny, Richard Kenyon, Sana Louhichi, Francesco Manzo, Carlo Mariconda, Reda Messikh,  Pierre Petit, Agoston Pisztora, Marie Théret, Daniele Tovazzi, Wei Zhou.


I have written five monographs:
Large deviations for three dimensional supercritical percolation, Astérisque 267, 177 pages, 2000
The Wulff crystal in Ising and Percolation models, Lecture notes in Mathematics 1878, 264 pages, 2006
On Cramér theory in infinite dimensions, Panoramas et Synthèses 23, 159 pages, 2007 (a small mistake)
Critical population and error threshold on the sharp peak landscape for a Moran model
, Memoirs of the American Mathematical Society 1096, 91 pages, 2015
The quasispecies equation and classical population models, with Joseba Dalmau, Probability Theory and Stochastic Modelling, Springer, 242 pages, 2022

Here is the list of my papers, and the corresponding pdf files organized by topic.
I did my PhD thesis on genetic algorithms in Montpellier under the supervision of Alain Berlinet.

My research effort is mainly aimed at proving that there is no percolation at the critical point in dimension 3.